D₇×C₂₂₅₁ #44538517

order	31514
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₂₅₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₂₂₅₁
unambiguous semidirect product	C₇⋊(C₂×C₂₂₅₁)

Fitting, socle, Hall	C₇×C₂₂₅₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₂₂₅₁

	subgroup	G/H
center, hypercenter	C₂₂₅₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₂₂₅₁
Frattini	C₁	G
Fitting, socle	C₇×C₂₂₅₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂₂₅₁

8 conjugacy classes of subgroups.

μ_t(G) = 15757

11255 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31514, 1);