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C₁₃×C₆₇⋊C₉ #21463202

order	7839
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₆₇⋊C₉
unambiguous semidirect product	C₆₇⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₆₇ ⋊ C₉×C₁₃
Hall	C₁₃×C₆₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₆₇⋊C₃
commutator, hypocenter	C₆₇	C₉×C₁₃
Frattini	C₃	C₁₃×C₆₇⋊C₃
Fitting, socle	C₃×C₁₃×C₆₇	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₃×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₃×C₆₇⋊C₉, C₁₃×D₆₇⋊C₉, D₁₃×C₆₇⋊C₉, …
maximal normal subgroup of	C₂×C₁₃×C₆₇⋊C₉, C₁₃×D₆₇⋊C₉, D₁₃×C₆₇⋊C₉, …
maximal quotient of	C₂×C₁₃×C₆₇⋊C₉, C₁₃×C₂²⋊(C₆₇⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7839, 3);