C₁₁×C₇⋊Dic₇ #14524159

order	2156
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₁×C₇⋊Dic₇
unambiguous semidirect product	C₇⋊(C₁₁×Dic₇)

derived, Sylow	C₇² ⋊ C₄×C₁₁
Hall	C₇²×C₁₁ ⋊ C₄

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 2156

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,18)(19,20)(21,22)(24,25)(26,27)(28,29);(23,24,26,28,29,27,25);(16,17,19,21,22,20,18)

572 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2156, 14);