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C₉×D₅₁₁ #22604083

order	9198
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₅₁₁

Splittings

Fitting, Hall	C₇×C₉×C₇₃ ⋊ C₂
derived, Hall	C₇×C₇₃ ⋊ C₂×C₉
Hall	C₉×C₇₃ ⋊ D₇
Sylow	C₇₃ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₇₃
Sylow	C₇ ⋊ C₉×D₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₁₁
commutator, hypocenter	C₇×C₇₃	C₂×C₉
Frattini	C₃	C₃×D₅₁₁
Fitting	C₇×C₉×C₇₃	C₂
socle	C₃×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2313 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₇₃, D₉×D₅₁₁, D₆₃⋊D₇₃, …
maximal normal subgroup of	C₉×D₇×D₇₃, D₉×D₅₁₁, D₆₃⋊D₇₃, …
maximal quotient of	C₉×Dic₅₁₁, C₂×C₉×D₅₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 8);