C₁₁×C₂²⋊C₂₇ #11924636

order	1188
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₂₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₁×C₂²⋊C₂₇
unambiguous semidirect product	C₂²⋊(C₁₁×C₂₇)
unambiguous semidirect product	(C₂²×C₁₁)⋊C₂₇

derived, Sylow	C₂² ⋊ C₁₁×C₂₇
Hall	C₂²×C₁₁ ⋊ C₂₇

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 594

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15)(16,17,20,18,21,26,23,28,33,19,22,27,24,29,34,31,36,39,25,30,35,32,37,40,38,41,42);(12,15)(13,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 6);