↑

Learn more

Refine search

Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
Abelian Cyclic Solvable Simple
Perfect Direct product Semidirect product Wreath product
Automorphism group Automorphisms Transitive degree Permutation degree
Minimal degree of $\C$-irrep Minimal degree of $\Q$-irrep Minimal degree of $\C$-rep Minimal degree of $\Q$-rep
Outer aut. group Outer automorphisms Metabelian Metacyclic
Almost simple Quasisimple A-group Z-group
Frattini subgroup Derived length Rank Schur multiplier
Supersolvable Monomial Rational
Number of subgroups Number of normal subgroups Number of conjugacy classes
Number of characteristic subgroups Number of autjugacy classes Number of divisions
Order statistics Order factorization Commutator length
Order
Sort order Select

Results (1-50 of 1192 matches)

Next   displayed columns for results
Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
12.1 $C_3:C_4$ $2^{2} \cdot 3$ $2^{2} \cdot 3$ $6$ $C_2$ $S_3$ $C_3$ $C_{4}$ Solvable - 2
12.2 $C_{12}$ $2^{2} \cdot 3$ $2^{2} \cdot 3$ $12$ $C_{12}$ $C_1$ $C_1$ $C_{12}$ Cyclic
12.3 $A_4$ $2^{2} \cdot 3$ $2 \cdot 3$ $4$ $C_1$ $A_4$ $C_2^2$ $C_{3}$ Solvable - 2
12.4 $D_6$ $2^{2} \cdot 3$ $2 \cdot 3$ $6$ $C_2$ $S_3$ $C_3$ $C_{2}^{2}$ Solvable - 2
12.5 $C_2\times C_6$ $2^{2} \cdot 3$ $2 \cdot 3$ $12$ $C_2\times C_6$ $C_1$ $C_1$ $C_{2} \times C_{6}$ Abelian - 2
18.1 $D_9$ $2 \cdot 3^{2}$ $2 \cdot 3^{2}$ $6$ $C_1$ $D_9$ $C_9$ $C_{2}$ Solvable - 2
18.2 $C_{18}$ $2 \cdot 3^{2}$ $2 \cdot 3^{2}$ $18$ $C_{18}$ $C_1$ $C_1$ $C_{18}$ Cyclic
18.3 $C_3\times S_3$ $2 \cdot 3^{2}$ $2 \cdot 3$ $9$ $C_3$ $S_3$ $C_3$ $C_{6}$ Solvable - 2
18.4 $C_3:S_3$ $2 \cdot 3^{2}$ $2 \cdot 3$ $6$ $C_1$ $C_3:S_3$ $C_3^2$ $C_{2}$ Solvable - 2
18.5 $C_3\times C_6$ $2 \cdot 3^{2}$ $2 \cdot 3$ $18$ $C_3\times C_6$ $C_1$ $C_1$ $C_{3} \times C_{6}$ Abelian - 2
20.1 $C_5:C_4$ $2^{2} \cdot 5$ $2^{2} \cdot 5$ $8$ $C_2$ $D_5$ $C_5$ $C_{4}$ Solvable - 2
20.2 $C_{20}$ $2^{2} \cdot 5$ $2^{2} \cdot 5$ $20$ $C_{20}$ $C_1$ $C_1$ $C_{20}$ Cyclic
20.3 $F_5$ $2^{2} \cdot 5$ $2^{2} \cdot 5$ $5$ $C_1$ $F_5$ $C_5$ $C_{4}$ Solvable - 2
20.4 $D_{10}$ $2^{2} \cdot 5$ $2 \cdot 5$ $8$ $C_2$ $D_5$ $C_5$ $C_{2}^{2}$ Solvable - 2
20.5 $C_2\times C_{10}$ $2^{2} \cdot 5$ $2 \cdot 5$ $20$ $C_2\times C_{10}$ $C_1$ $C_1$ $C_{2} \times C_{10}$ Abelian - 2
28.1 $C_7:C_4$ $2^{2} \cdot 7$ $2^{2} \cdot 7$ $10$ $C_2$ $D_7$ $C_7$ $C_{4}$ Solvable - 2
28.2 $C_{28}$ $2^{2} \cdot 7$ $2^{2} \cdot 7$ $28$ $C_{28}$ $C_1$ $C_1$ $C_{28}$ Cyclic
28.3 $D_{14}$ $2^{2} \cdot 7$ $2 \cdot 7$ $10$ $C_2$ $D_7$ $C_7$ $C_{2}^{2}$ Solvable - 2
28.4 $C_2\times C_{14}$ $2^{2} \cdot 7$ $2 \cdot 7$ $28$ $C_2\times C_{14}$ $C_1$ $C_1$ $C_{2} \times C_{14}$ Abelian - 2
36.1 $C_9:C_4$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ $12$ $C_2$ $D_9$ $C_9$ $C_{4}$ Solvable - 2
36.2 $C_{36}$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ $36$ $C_{36}$ $C_1$ $C_1$ $C_{36}$ Cyclic
36.3 $C_2^2:C_9$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ $12$ $C_3$ $A_4$ $C_2^2$ $C_{9}$ Solvable - 2
36.4 $D_{18}$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ $12$ $C_2$ $D_9$ $C_9$ $C_{2}^{2}$ Solvable - 2
36.5 $C_2\times C_{18}$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ $36$ $C_2\times C_{18}$ $C_1$ $C_1$ $C_{2} \times C_{18}$ Abelian - 2
36.6 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $18$ $C_6$ $S_3$ $C_3$ $C_{12}$ Solvable - 2
36.7 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $12$ $C_2$ $C_3:S_3$ $C_3^2$ $C_{4}$ Solvable - 2
36.8 $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $36$ $C_3\times C_{12}$ $C_1$ $C_1$ $C_{3} \times C_{12}$ Abelian - 2
36.9 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $6$ $C_1$ $C_3^2:C_4$ $C_3^2$ $C_{4}$ Solvable - 2
36.10 $S_3^2$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $9$ $C_1$ $S_3^2$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
36.11 $C_3\times A_4$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $12$ $C_3$ $A_4$ $C_2^2$ $C_{3}^{2}$ Solvable - 2
36.12 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $18$ $C_6$ $S_3$ $C_3$ $C_{2} \times C_{6}$ Solvable - 2
36.13 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $12$ $C_2$ $C_3:S_3$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
36.14 $C_6^2$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $36$ $C_6^2$ $C_1$ $C_1$ $C_{6}^{2}$ Abelian - 2
44.1 $C_{11}:C_4$ $2^{2} \cdot 11$ $2^{2} \cdot 11$ $14$ $C_2$ $D_{11}$ $C_{11}$ $C_{4}$ Solvable - 2
44.2 $C_{44}$ $2^{2} \cdot 11$ $2^{2} \cdot 11$ $44$ $C_{44}$ $C_1$ $C_1$ $C_{44}$ Cyclic
44.3 $D_{22}$ $2^{2} \cdot 11$ $2 \cdot 11$ $14$ $C_2$ $D_{11}$ $C_{11}$ $C_{2}^{2}$ Solvable - 2
44.4 $C_2\times C_{22}$ $2^{2} \cdot 11$ $2 \cdot 11$ $44$ $C_2\times C_{22}$ $C_1$ $C_1$ $C_{2} \times C_{22}$ Abelian - 2
45.1 $C_{45}$ $3^{2} \cdot 5$ $3^{2} \cdot 5$ $45$ $C_{45}$ $C_1$ $C_1$ $C_{45}$ Cyclic
45.2 $C_3\times C_{15}$ $3^{2} \cdot 5$ $3 \cdot 5$ $45$ $C_3\times C_{15}$ $C_1$ $C_1$ $C_{3} \times C_{15}$ Abelian - 2
50.1 $D_{25}$ $2 \cdot 5^{2}$ $2 \cdot 5^{2}$ $14$ $C_1$ $D_{25}$ $C_{25}$ $C_{2}$ Solvable - 2
50.2 $C_{50}$ $2 \cdot 5^{2}$ $2 \cdot 5^{2}$ $50$ $C_{50}$ $C_1$ $C_1$ $C_{50}$ Cyclic
50.3 $C_5\times D_5$ $2 \cdot 5^{2}$ $2 \cdot 5$ $20$ $C_5$ $D_5$ $C_5$ $C_{10}$ Solvable - 2
50.4 $C_5:D_5$ $2 \cdot 5^{2}$ $2 \cdot 5$ $14$ $C_1$ $C_5:D_5$ $C_5^2$ $C_{2}$ Solvable - 2
50.5 $C_5\times C_{10}$ $2 \cdot 5^{2}$ $2 \cdot 5$ $50$ $C_5\times C_{10}$ $C_1$ $C_1$ $C_{5} \times C_{10}$ Abelian - 2
52.1 $C_{13}:C_4$ $2^{2} \cdot 13$ $2^{2} \cdot 13$ $16$ $C_2$ $D_{13}$ $C_{13}$ $C_{4}$ Solvable - 2
52.2 $C_{52}$ $2^{2} \cdot 13$ $2^{2} \cdot 13$ $52$ $C_{52}$ $C_1$ $C_1$ $C_{52}$ Cyclic
52.3 $C_{13}:C_4$ $2^{2} \cdot 13$ $2^{2} \cdot 13$ $7$ $C_1$ $C_{13}:C_4$ $C_{13}$ $C_{4}$ Solvable - 2
52.4 $D_{26}$ $2^{2} \cdot 13$ $2 \cdot 13$ $16$ $C_2$ $D_{13}$ $C_{13}$ $C_{2}^{2}$ Solvable - 2
52.5 $C_2\times C_{26}$ $2^{2} \cdot 13$ $2 \cdot 13$ $52$ $C_2\times C_{26}$ $C_1$ $C_1$ $C_{2} \times C_{26}$ Abelian - 2
63.1 $C_7:C_9$ $3^{2} \cdot 7$ $3^{2} \cdot 7$ $15$ $C_3$ $C_7:C_3$ $C_7$ $C_{9}$ Solvable - 2
Next   displayed columns for results