C₂₃×C₁₁⋊C₅ #11929628

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

Aliases

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

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

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

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 253

A minimal faithful permutation representation — 2 generators on 34 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1265, 2);