D₅×C₂₅₅₁ #38784167

order	25510
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅₅₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₂₅₅₁
unambiguous semidirect product	C₅⋊(C₂×C₂₅₅₁)

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

	subgroup	G/H
center, hypercenter	C₂₅₅₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₂₅₅₁
Frattini	C₁	G
Fitting, socle	C₅×C₂₅₅₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂₅₅₁

8 conjugacy classes of subgroups.

μ_t(G) = 12755

10204 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25510, 3);