C₅²×ΓL(1,𝔽₈)×C₄₇ #37590525

order	24675
automorphism	?
homology	Abelianization (H₁) = C₃×C₅²×C₄₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×ΓL(1,𝔽₈)×C₄₇
unambiguous semidirect product	C₇⋊(C₃×C₅²×C₄₇)
unambiguous semidirect product	(C₅×C₇)⋊(C₃×C₅×C₄₇)
unambiguous semidirect product	(C₇×C₄₇)⋊(C₃×C₅²)
unambiguous semidirect product	(C₅×C₇×C₄₇)⋊(C₃×C₅)

	subgroup	G/H
center, hypercenter	C₅²×C₄₇	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₅²×C₄₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₄₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₅²×C₄₇

64 conjugacy classes of subgroups.

μ_t(G) = 8225

5875 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24675, 6);