D₅×C₅⋊D₅ #92565

order	500
isoclinism	isoclinic class of D₅×C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₅×C₅⋊D₅
unambiguous semidirect product	(C₅×D₅)⋊D₅
unambiguous semidirect product	(C₅⋊(C₅⋊D₅))⋊C₂

C₅³ ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅³	C₂²
LCS	G ▷ C₅³
UCS	C₁

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 50

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(500, 51);