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C₁₃×D₃₃₃ #22575858

order	8658
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₃₃₃
unambiguous semidirect product	C₉⋊(C₁₃×D₃₇)
unambiguous semidirect product	C₃₇⋊(C₁₃×D₉)

Splittings

Fitting, Hall	C₉×C₁₃×C₃₇ ⋊ C₂
derived, Hall	C₉×C₃₇ ⋊ C₂×C₁₃
Hall	C₁₃×C₃₇ ⋊ D₉
Hall	C₉×C₁₃ ⋊ D₃₇
Sylow	C₃₇ ⋊ C₁₃×D₉
Sylow	C₉ ⋊ C₁₃×D₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₃₃₃
commutator, hypocenter	C₉×C₃₇	C₂×C₁₃
Frattini	C₃	C₁₃×D₁₁₁
Fitting	C₉×C₁₃×C₃₇	C₂
socle	C₃×C₁₃×C₃₇	D₃
LCS	G ▷ C₉×C₃₇
UCS	C₁ ◁ C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₉×D₃₇, D₁₃×D₃₃₃, D₁₁₇⋊D₃₇, …
maximal normal subgroup of	C₁₃×D₉×D₃₇, D₁₃×D₃₃₃, D₁₁₇⋊D₃₇, …
maximal quotient of	C₁₃×Dic₃₃₃, C₂×C₁₃×D₃₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8658, 10);