C₂³×C₁₁⋊C₅ #89191

order	440
isoclinism	isoclinic class of C₁₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

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

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

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

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 3 generators on 17 points:

(5,6)(8,9,11,14,13)(10,12,16,17,15);(3,4)(7,8,10,13,9,11,15,17,12,14,16);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 44);