C₂×C₅⋊D₅×C₂₅₁ #38737250

order	25100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₂₅₁
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₂₅₁)

	subgroup	G/H
center, hypercenter	C₂×C₂₅₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₂₅₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₅₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₂₅₁

80 conjugacy classes of subgroups.

μ_t(G) = 12550

7028 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25100, 54);