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C₇₃×C₁₃⋊C₉ #22555433

order	8541
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₃×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₉×C₇₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₇₃
Frattini	C₃	C₁₃⋊C₃×C₇₃
Fitting, socle	C₃×C₁₃×C₇₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1533 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇₃×C₁₃⋊C₉, C₁₃⋊C₉×D₇₃, C₇₃×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₇₃×C₁₃⋊C₉, C₁₃⋊C₉×D₇₃, C₇₃×D₁₃⋊C₉, …
maximal quotient of	C₂×C₇₃×C₁₃⋊C₉, C₇₃×C₂²⋊(C₁₃⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8541, 2);