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C₉×D₃₉₁ #20296379

order	7038
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₃₉₁
unambiguous semidirect product	C₁₇⋊(C₉×D₂₃)
unambiguous semidirect product	C₂₃⋊(C₉×D₁₇)

Splittings

Fitting, Hall	C₉×C₁₇×C₂₃ ⋊ C₂
derived, Hall	C₁₇×C₂₃ ⋊ C₂×C₉
Hall	C₉×C₂₃ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ D₂₃
Sylow	C₂₃ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₉×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₃₉₁
commutator, hypocenter	C₁₇×C₂₃	C₂×C₉
Frattini	C₃	C₃×D₃₉₁
Fitting	C₉×C₁₇×C₂₃	C₂
socle	C₃×C₁₇×C₂₃	C₂×C₃
LCS	G ▷ C₁₇×C₂₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1773 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×D₂₃, D₉×D₃₉₁, D₁₅₃⋊D₂₃, …
maximal normal subgroup of	C₉×D₁₇×D₂₃, D₉×D₃₉₁, D₁₅₃⋊D₂₃, …
maximal quotient of	C₉×Dic₃₉₁, C₂×C₉×D₃₉₁, C₅×C₉×D₃₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7038, 4);