C₂×C₅⋊#226 #91951

order	480
isoclinism	isoclinic class of C₅⋊#226
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅⋊#226
unambiguous semidirect product	(C₂×C₅)⋊#226

	subgroup	G/H
center, hypercenter	C₂²	C₅⋊S₄
commutator, cosocle, hypocenter	C₅×SL(2,𝔽₃)	C₂²
Frattini	C₂	C₂×C₅⋊S₄
Fitting	C₂×C₅×Q₈	D₃
socle	C₂²×C₅	S₄
prime radical	C₂×C₅×SL(2,𝔽₃)	C₂
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1027);