C₅⋊S₅ #10597164

order	600
isoclinism	isoclinic class of C₅⋊S₅
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₅⋊S₅
unambiguous semidirect product	A₅⋊D₅

Fitting	C₅ ⋊ S₅
socle, derived	C₅×A₅ ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	C₅×A₅	C₂
Fitting	C₅	S₅
LCS	G ▷ C₅×A₅
UCS	C₁

39 conjugacy classes of subgroups.

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 25

A minimal faithful permutation representation — 2 generators on 10 points:

(1,4)(2,3)(7,9,8,10);(2,5)(3,4)(6,8,7)(9,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 145);