C₅×D₉×C₂₆₉ #37564160

order	24210
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₆₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₉×C₂₆₉
unambiguous semidirect product	C₉⋊(C₂×C₅×C₂₆₉)

	subgroup	G/H
center, hypercenter	C₅×C₂₆₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₂₆₉
Frattini	C₃	C₅×D₃×C₂₆₉
Fitting	C₅×C₉×C₂₆₉	C₂
socle	C₃×C₅×C₂₆₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₂₆₉

24 conjugacy classes of subgroups.

μ_t(G) = 12105

8070 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24210, 5);