C₅×C₅⋊(C₅⋊D₅) #11929404

order	1250
isoclinism	isoclinic class of C₅⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₅³

Aliases

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

Fitting, socle, Sylow	C₅⁴ ⋊ C₂
derived	C₅³ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	C₅⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₅³	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅⁴	C₂
LCS	G ▷ C₅³
UCS	C₁ ◁ C₅

752 conjugacy classes of subgroups.

μ_t(G) = 250

320 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₅×D₅×C₅⋊D₅, D₅×C₅⋊(C₅⋊D₅), #72228993
maximal normal subgroup of	C₅×D₅×C₅⋊D₅, D₅×C₅⋊(C₅⋊D₅), #72228993

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1250, 55);