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C₉×D₅₇₇ #23780707

order	10386
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₅₇₇

Splittings

Fitting, Hall	C₉×C₅₇₇ ⋊ C₂
derived, Sylow	C₅₇₇ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₇₇
commutator, hypocenter	C₅₇₇	C₂×C₉
Frattini	C₃	C₃×D₅₇₇
Fitting	C₉×C₅₇₇	C₂
socle, cosocle	C₃×C₅₇₇	C₂×C₃
prime radical	C₃×D₅₇₇	C₃
LCS	G ▷ C₅₇₇
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2610 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#14556313, C₉⋊#14556313, D₉×D₅₇₇, …
maximal normal subgroup of	C₉×#14556313, C₉⋊#14556313, D₉×D₅₇₇, …
maximal quotient of	C₉×Dic₅₇₇, C₂×C₉×D₅₇₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10386, 5);