C₇⋊D₇×C₂₅₁ #37589730

order	24598
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅₁ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₂₅₁
unambiguous semidirect product	C₇⋊(D₇×C₂₅₁)

Fitting, socle, Hall	C₇²×C₂₅₁ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₂₅₁

	subgroup	G/H
center, hypercenter	C₂₅₁	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₂₅₁
Frattini	C₁	G
Fitting, socle	C₇²×C₂₅₁	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂₅₁

40 conjugacy classes of subgroups.

μ_t(G) = 12299

6526 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24598, 9);