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C₉×C₂₈₁⋊C₇ #31799261

order	17703
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₂₈₁⋊C₇
unambiguous semidirect product	C₂₈₁⋊(C₇×C₉)
unambiguous semidirect product	(C₉×C₂₈₁)⋊C₇

Splittings

Fitting, Hall	C₉×C₂₈₁ ⋊ C₇
derived, Sylow	C₂₈₁ ⋊ C₇×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₂₈₁⋊C₇
commutator, hypocenter	C₂₈₁	C₇×C₉
Frattini	C₃	C₃×C₂₈₁⋊C₇
Fitting	C₉×C₂₈₁	C₇
socle, cosocle	C₃×C₂₈₁	C₃×C₇
prime radical	C₃×C₂₈₁⋊C₇	C₃
LCS	G ▷ C₂₈₁
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2529

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₉×C₂₈₁⋊C₇, C₉×D₂₈₁⋊C₇, D₉×C₂₈₁⋊C₇, …
maximal normal subgroup of	C₂×C₉×C₂₈₁⋊C₇, C₉×D₂₈₁⋊C₇, D₉×C₂₈₁⋊C₇, …
maximal quotient of	C₂×C₉×C₂₈₁⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17703, 2);