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C₉×D₃₈₅ #20294124

order	6930
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₃₈₅
unambiguous semidirect product	C₅⋊(C₉×D₇₇)
unambiguous semidirect product	C₁₁⋊(C₉×D₃₅)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₁₁ ⋊ C₂
derived, Hall	C₅×C₇×C₁₁ ⋊ C₂×C₉
Hall	C₇×C₉×C₁₁ ⋊ D₅
Hall	C₅×C₉×C₁₁ ⋊ D₇
Hall	C₅×C₇×C₉ ⋊ D₁₁
Hall	C₉×C₁₁ ⋊ D₃₅
Hall	C₇×C₁₁ ⋊ C₉×D₅
Hall	C₇×C₉ ⋊ D₅₅
Hall	C₅×C₁₁ ⋊ C₉×D₇
Hall	C₅×C₉ ⋊ D₇₇
Hall	C₅×C₇ ⋊ C₉×D₁₁
Sylow	C₁₁ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ C₉×D₅₅
Sylow	C₅ ⋊ C₉×D₇₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₃₈₅
commutator, hypocenter	C₅×C₇×C₁₁	C₂×C₉
Frattini	C₃	C₃×D₃₈₅
Fitting	C₅×C₇×C₉×C₁₁	C₂
socle	C₃×C₅×C₇×C₁₁	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1746 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₁×D₃₅, C₉×D₇×D₅₅, C₉×D₅×D₇₇, …
maximal normal subgroup of	C₉×D₁₁×D₃₅, C₉×D₇×D₅₅, C₉×D₅×D₇₇, …
maximal quotient of	C₉×Dic₃₈₅, C₂×C₉×D₃₈₅, C₉×D₁₉₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 11);