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C₉×D₉₄₉ #30685146

order	17082
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₉₄₉

Splittings

Fitting, Hall	C₉×C₁₃×C₇₃ ⋊ C₂
derived, Hall	C₁₃×C₇₃ ⋊ C₂×C₉
Hall	C₉×C₇₃ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₇₃
Sylow	C₇₃ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₉₄₉
commutator, hypocenter	C₁₃×C₇₃	C₂×C₉
Frattini	C₃	C₃×D₉₄₉
Fitting	C₉×C₁₃×C₇₃	C₂
socle, cosocle	C₃×C₁₃×C₇₃	C₂×C₃
prime radical	C₃×D₉₄₉	C₃
LCS	G ▷ C₁₃×C₇₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8541

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#16838291, C₉×#16838292, C₉×D₁₃×D₇₃, …
maximal normal subgroup of	C₉×#16838291, C₉×#16838292, C₉×D₁₃×D₇₃, …
maximal quotient of	C₉×Dic₉₄₉, C₂×C₉×D₉₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17082, 8);