C₅⋊D₅×C₇₂₇ #49138233

order	36350
automorphism	?
homology	Abelianization (H₁) = C₂×C₇₂₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅⋊D₅×C₇₂₇
unambiguous semidirect product	C₅⋊(D₅×C₇₂₇)

Fitting, socle, Hall	C₅²×C₇₂₇ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₇₂₇

	subgroup	G/H
center, hypercenter	C₇₂₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇₂₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇₂₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₇₂₇

32 conjugacy classes of subgroups.

μ_t(G) = 18175

10178 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36350, 9);