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C₃₇×D₁₃⋊C₉ #22575866

order	8658
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₃₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₃₇)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₃₇
Hall	C₃₇×C₁₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₃₇ ⋊ C₉
Hall	C₁₃×C₃₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₃₇
Hall	D₁₃ ⋊ C₉×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₃₇
Frattini	C₃	C₃₇×D₁₃⋊C₃
Fitting, socle	C₃×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₃₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

888 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#261⋊C₉, #31772762, D₃₇×D₁₃⋊C₉, …
maximal normal subgroup of	C₃₇×#261⋊C₉, #31772762, D₃₇×D₁₃⋊C₉, …
maximal quotient of	C₃₇×Dic₁₃⋊C₉, C₂×C₃₇×D₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8658, 18);