C₂×C₃×D₂₃×C₈₉ #37589571

order	24564
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₂₃×C₈₉
unambiguous semidirect product	C₂₃⋊(C₂²×C₃×C₈₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₂×C₃×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈₉	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₃×C₈₉	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃×C₈₉

40 conjugacy classes of subgroups.

μ_t(G) = 12282

6942 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24564, 23);