C₂×C₂₅₅₁⋊C₅ #38784166

order	25510
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₅₅₁⋊C₅
unambiguous semidirect product	(C₂×C₂₅₅₁)⋊C₅

Fitting, socle, Hall	C₂×C₂₅₅₁ ⋊ C₅
derived, Sylow	C₂₅₅₁ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₂	C₂₅₅₁⋊C₅
commutator, cosocle, hypocenter	C₂₅₅₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₂₅₅₁	C₅
LCS	G ▷ C₂₅₅₁
UCS	C₁ ◁ C₂

8 conjugacy classes of subgroups.

μ_t(G) = 5102

1030 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25510, 2);