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C₉×D₄₈₁ #22575856

order	8658
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₄₈₁

Splittings

Fitting, Hall	C₉×C₁₃×C₃₇ ⋊ C₂
derived, Hall	C₁₃×C₃₇ ⋊ C₂×C₉
Hall	C₉×C₃₇ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₃₇
Sylow	C₃₇ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₄₈₁
commutator, hypocenter	C₁₃×C₃₇	C₂×C₉
Frattini	C₃	C₃×D₄₈₁
Fitting	C₉×C₁₃×C₃₇	C₂
socle	C₃×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#14515321, C₉×#14515320, C₉×D₁₃×D₃₇, …
maximal normal subgroup of	C₉×#14515321, C₉×#14515320, C₉×D₁₃×D₃₇, …
maximal quotient of	C₉×Dic₄₈₁, C₂×C₉×D₄₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8658, 8);