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C₉×D₉₅₉ #31772115

order	17262
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₉₅₉
unambiguous semidirect product	C₁₃₇⋊(C₉×D₇)

Splittings

Fitting, Hall	C₇×C₉×C₁₃₇ ⋊ C₂
derived, Hall	C₇×C₁₃₇ ⋊ C₂×C₉
Hall	C₉×C₁₃₇ ⋊ D₇
Sylow	C₁₃₇ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₃₇
Sylow	C₇ ⋊ C₉×D₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₉₅₉
commutator, hypocenter	C₇×C₁₃₇	C₂×C₉
Frattini	C₃	C₃×D₉₅₉
Fitting	C₇×C₉×C₁₃₇	C₂
socle, cosocle	C₃×C₇×C₁₃₇	C₂×C₃
prime radical	C₃×D₉₅₉	C₃
LCS	G ▷ C₇×C₁₃₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8631

Conjugacy classes & character table

4329 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₃₇, D₉×D₉₅₉, D₆₃⋊D₁₃₇, …
maximal normal subgroup of	C₉×D₇×D₁₃₇, D₉×D₉₅₉, D₆₃⋊D₁₃₇, …
maximal quotient of	C₉×Dic₉₅₉, C₂×C₉×D₉₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17262, 5);