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C₉×D₁₃×C₇₃ #30685145

order	17082
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₃×C₇₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₇₃	D₁₃
commutator, hypocenter	C₁₃	C₂×C₉×C₇₃
Frattini	C₃	C₃×D₁₃×C₇₃
Fitting	C₉×C₁₃×C₇₃	C₂
socle	C₃×C₁₃×C₇₃	C₂×C₃
prime radical	C₃×D₁₃×C₇₃	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₇₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉×C₇₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8541

Conjugacy classes & character table

5256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#261×C₇₃, C₉×#16838293, C₉×D₁₃×D₇₃, …
maximal normal subgroup of	C₉×#261×C₇₃, C₉×#16838293, C₉×D₁₃×D₇₃, …
maximal quotient of	C₉×Dic₁₃×C₇₃, C₂×C₉×D₁₃×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17082, 7);