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C₉×D₉₅₃ #31769739

order	17154
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₉₅₃
unambiguous semidirect product	C₉₅₃⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₉₅₃ ⋊ C₂
derived, Sylow	C₉₅₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₉₅₃
commutator, hypocenter	C₉₅₃	C₂×C₉
Frattini	C₃	C₃×D₉₅₃
Fitting	C₉×C₉₅₃	C₂
socle, cosocle	C₃×C₉₅₃	C₂×C₃
prime radical	C₃×D₉₅₃	C₃
LCS	G ▷ C₉₅₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8577

Conjugacy classes & character table

4302 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#16838374, C₉⋊#16838374, D₉×D₉₅₃, …
maximal normal subgroup of	C₉×#16838374, C₉⋊#16838374, D₉×D₉₅₃, …
maximal quotient of	C₉×Dic₉₅₃, C₂×C₉×D₉₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17154, 3);