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C₇₉×C₁₃⋊C₉ #22604453

order	9243
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₉×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₉×C₇₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₇₉
Hall	C₁₃×C₇₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₇₉
Frattini	C₃	C₁₃⋊C₃×C₇₉
Fitting, socle	C₃×C₁₃×C₇₉	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇₉×C₁₃⋊C₉, C₁₃⋊C₉×D₇₉, C₇₉×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₇₉×C₁₃⋊C₉, C₁₃⋊C₉×D₇₉, C₇₉×D₁₃⋊C₉, …
maximal quotient of	C₂×C₇₉×C₁₃⋊C₉, C₇₉×C₂²⋊(C₁₃⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 4);