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C₆₇×C₁₃⋊C₉ #21463201

order	7839
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7839, 2);