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C₆₇×D₁₃⋊C₉ #30627896

order	15678
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₆₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₆₇)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₆₇
Hall	C₆₇×C₁₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₆₇ ⋊ C₉
Hall	C₁₃×C₆₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₆₇
Hall	D₁₃ ⋊ C₉×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₆₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₆₇
Frattini	C₃	C₆₇×D₁₃⋊C₃
Fitting, socle	C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₃×D₁₃×C₆₇	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₆₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7839

Conjugacy classes & character table

1608 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₆₇×#261⋊C₉, #44535595, D₆₇×D₁₃⋊C₉, …
maximal normal subgroup of	C₆₇×#261⋊C₉, #44535595, D₆₇×D₁₃⋊C₉, …
maximal quotient of	C₆₇×Dic₁₃⋊C₉, C₂×C₆₇×D₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15678, 18);