C₁₁²×C₂₉⋊C₇ #37589548

order	24563
automorphism	?
homology	Abelianization (H₁) = C₇×C₁₁² · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₁₁²×C₂₉⋊C₇
unambiguous semidirect product	C₂₉⋊(C₇×C₁₁²)
unambiguous semidirect product	(C₁₁×C₂₉)⋊(C₇×C₁₁)
unambiguous semidirect product	(C₁₁²×C₂₉)⋊C₇

Fitting, socle, Hall	C₁₁²×C₂₉ ⋊ C₇
derived, Sylow	C₂₉ ⋊ C₇×C₁₁²

	subgroup	G/H
center, hypercenter	C₁₁²	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₇×C₁₁²
Frattini	C₁	G
Fitting, socle	C₁₁²×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₁₁²

56 conjugacy classes of subgroups.

μ_t(G) = 3509

1331 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24563, 4);