C₅×C₂₃⋊C₁₁ #11929627

order	1265
isoclinism	isoclinic class of C₂₃⋊C₁₁
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₃⋊C₁₁
unambiguous semidirect product	C₂₃⋊(C₅×C₁₁)
unambiguous semidirect product	(C₅×C₂₃)⋊C₁₁

Fitting, socle, Hall	C₅×C₂₃ ⋊ C₁₁
derived, Sylow	C₂₃ ⋊ C₅×C₁₁

	subgroup	G/H
center, hypercenter	C₅	C₂₃⋊C₁₁
commutator, cosocle, hypocenter	C₂₃	C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₂₃	C₁₁
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 115

A minimal faithful permutation representation — 2 generators on 28 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1265, 1);