C₂×C₅⋊D₅×C₂₂₇ #36384207

order	22700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₂₇ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₂₂₇
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₂₂₇)

	subgroup	G/H
center, hypercenter	C₂×C₂₂₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₂₂₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₂₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₂₂₇

80 conjugacy classes of subgroups.

μ_t(G) = 11350

6356 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22700, 35);