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C₉×D₅₉₃ #24922656

order	10674
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅₉₃
unambiguous semidirect product	C₅₉₃⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₅₉₃ ⋊ C₂
derived, Sylow	C₅₉₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₉₃
commutator, hypocenter	C₅₉₃	C₂×C₉
Frattini	C₃	C₃×D₅₉₃
Fitting	C₉×C₅₉₃	C₂
socle, cosocle	C₃×C₅₉₃	C₂×C₃
prime radical	C₃×D₅₉₃	C₃
LCS	G ▷ C₅₉₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2682 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#14558631, C₉⋊#14558631, D₉×D₅₉₃, …
maximal normal subgroup of	C₉×#14558631, C₉⋊#14558631, D₉×D₅₉₃, …
maximal quotient of	C₉×Dic₅₉₃, C₂×C₉×D₅₉₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10674, 3);