Abstract group search results

Note: Search results may be incomplete due to uncomputed quantities: Automorphism group order (4830 objects)

Results (17 matches)

 

Label	Name	Order	Exponent	Nilp. class	Der. length	Comp. length	Rank	$\card{\mathrm{conj}(G)}$	Subgroups	Subgroup classes	Normal subgroups	Center	Central quotient	Commutator	Abelianization	$\card{\mathrm{Aut}(G)}$	$\card{\mathrm{Out}(G)}$	Tr. deg	Perm. deg	$\C$-irrep deg	$\R$-irrep deg	$\Q$-irrep deg	$\C$-rep deg	$\R$-rep deg	$\Q$-rep deg	Type - length
14.1	$D_7$	$2 \cdot 7$	$2 \cdot 7$	$-1$	$2$	$2$	$2$	$5$	$10$	$4$	$3$	$C_1$	$D_7$	$C_7$	$C_{2}$	$2 \cdot 3 \cdot 7$	$3$	$7$	$7$	$2$	$2$	$6$	$2$	$2$	$6$	Solvable - 2
21.1	$C_7:C_3$	$3 \cdot 7$	$3 \cdot 7$	$-1$	$2$	$2$	$2$	$5$	$10$	$4$	$3$	$C_1$	$C_7:C_3$	$C_7$	$C_{3}$	$2 \cdot 3 \cdot 7$	$2$	$7$	$7$	$3$	$6$	$6$	$3$	$6$	$6$	Solvable - 2
22.1	$D_{11}$	$2 \cdot 11$	$2 \cdot 11$	$-1$	$2$	$2$	$2$	$7$	$14$	$4$	$3$	$C_1$	$D_{11}$	$C_{11}$	$C_{2}$	$2 \cdot 5 \cdot 11$	$5$	$11$	$11$	$2$	$2$	$10$	$2$	$2$	$10$	Solvable - 2
30.2	$C_3\times D_5$	$2 \cdot 3 \cdot 5$	$2 \cdot 3 \cdot 5$	$-1$	$2$	$3$	$2$	$12$	$16$	$8$	$6$	$C_3$	$D_5$	$C_5$	$C_{6}$	$2^{3} \cdot 5$	$2^{2}$	$15$	$8$	$2$	$4$	$8$	$2$	$4$	$6$	Solvable - 2
30.3	$D_{15}$	$2 \cdot 3 \cdot 5$	$2 \cdot 3 \cdot 5$	$-1$	$2$	$3$	$2$	$9$	$28$	$8$	$5$	$C_1$	$D_{15}$	$C_{15}$	$C_{2}$	$2^{3} \cdot 3 \cdot 5$	$2^{2}$	$15$	$8$	$2$	$2$	$8$	$2$	$2$	$6$	Solvable - 2
42.1	$F_7$	$2 \cdot 3 \cdot 7$	$2 \cdot 3 \cdot 7$	$-1$	$2$	$3$	$2$	$7$	$26$	$8$	$5$	$C_1$	$F_7$	$C_7$	$C_{6}$	$2 \cdot 3 \cdot 7$	$1$	$7$	$7$	$6$	$6$	$6$	$6$	$6$	$6$	Solvable - 2
42.2	$C_7:C_6$	$2 \cdot 3 \cdot 7$	$2 \cdot 3 \cdot 7$	$-1$	$2$	$3$	$2$	$10$	$20$	$8$	$6$	$C_2$	$C_7:C_3$	$C_7$	$C_{6}$	$2 \cdot 3 \cdot 7$	$2$	$14$	$9$	$3$	$6$	$6$	$3$	$6$	$6$	Solvable - 2
42.3	$S_3\times C_7$	$2 \cdot 3 \cdot 7$	$2 \cdot 3 \cdot 7$	$-1$	$2$	$3$	$2$	$21$	$12$	$8$	$6$	$C_7$	$S_3$	$C_3$	$C_{14}$	$2^{2} \cdot 3^{2}$	$2 \cdot 3$	$21$	$10$	$2$	$4$	$12$	$2$	$4$	$8$	Solvable - 2
42.4	$C_3\times D_7$	$2 \cdot 3 \cdot 7$	$2 \cdot 3 \cdot 7$	$-1$	$2$	$3$	$2$	$15$	$20$	$8$	$6$	$C_3$	$D_7$	$C_7$	$C_{6}$	$2^{2} \cdot 3 \cdot 7$	$2 \cdot 3$	$21$	$10$	$2$	$4$	$12$	$2$	$4$	$8$	Solvable - 2
55.1	$C_{11}:C_5$	$5 \cdot 11$	$5 \cdot 11$	$-1$	$2$	$2$	$2$	$7$	$14$	$4$	$3$	$C_1$	$C_{11}:C_5$	$C_{11}$	$C_{5}$	$2 \cdot 5 \cdot 11$	$2$	$11$	$11$	$5$	$10$	$10$	$5$	$10$	$10$	Solvable - 2
66.1	$S_3\times C_{11}$	$2 \cdot 3 \cdot 11$	$2 \cdot 3 \cdot 11$	$-1$	$2$	$3$	$2$	$33$	$12$	$8$	$6$	$C_{11}$	$S_3$	$C_3$	$C_{22}$	$2^{2} \cdot 3 \cdot 5$	$2 \cdot 5$	$33$	$14$	$2$	$4$	$20$	$2$	$4$	$12$	Solvable - 2
70.1	$C_7\times D_5$	$2 \cdot 5 \cdot 7$	$2 \cdot 5 \cdot 7$	$-1$	$2$	$3$	$2$	$28$	$16$	$8$	$6$	$C_7$	$D_5$	$C_5$	$C_{14}$	$2^{3} \cdot 3 \cdot 5$	$2^{2} \cdot 3$	$35$	$12$	$2$	$4$	$24$	$2$	$4$	$10$	Solvable - 2
78.3	$S_3\times C_{13}$	$2 \cdot 3 \cdot 13$	$2 \cdot 3 \cdot 13$	$-1$	$2$	$3$	$2$	$39$	$12$	$8$	$6$	$C_{13}$	$S_3$	$C_3$	$C_{26}$	$2^{3} \cdot 3^{2}$	$2^{2} \cdot 3$	$39$	$16$	$2$	$4$	$24$	$2$	$4$	$14$	Solvable - 2
102.1	$S_3\times C_{17}$	$2 \cdot 3 \cdot 17$	$2 \cdot 3 \cdot 17$	$-1$	$2$	$3$	$2$	$51$	$12$	$8$	$6$	$C_{17}$	$S_3$	$C_3$	$C_{34}$	$2^{5} \cdot 3$	$2^{4}$	$51$	$20$	$2$	$4$	$32$	$2$	$4$	$18$	Solvable - 2
110.1	$F_{11}$	$2 \cdot 5 \cdot 11$	$2 \cdot 5 \cdot 11$	$-1$	$2$	$3$	$2$	$11$	$38$	$8$	$5$	$C_1$	$F_{11}$	$C_{11}$	$C_{10}$	$2 \cdot 5 \cdot 11$	$1$	$11$	$11$	$10$	$10$	$10$	$10$	$10$	$10$	Solvable - 2
110.2	$C_{11}:C_{10}$	$2 \cdot 5 \cdot 11$	$2 \cdot 5 \cdot 11$	$-1$	$2$	$3$	$2$	$14$	$28$	$8$	$6$	$C_2$	$C_{11}:C_5$	$C_{11}$	$C_{10}$	$2 \cdot 5 \cdot 11$	$2$	$22$	$13$	$5$	$10$	$10$	$5$	$10$	$10$	Solvable - 2
114.3	$S_3\times C_{19}$	$2 \cdot 3 \cdot 19$	$2 \cdot 3 \cdot 19$	$-1$	$2$	$3$	$2$	$57$	$12$	$8$	$6$	$C_{19}$	$S_3$	$C_3$	$C_{38}$	$2^{2} \cdot 3^{3}$	$2 \cdot 3^{2}$	$57$	$22$	$2$	$4$	$36$	$2$	$4$	$20$	Solvable - 2