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D₁₃×C₄₃⋊C₉ #23758453

order	10062
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

D₁₃×C₄₃⋊C₉

Splittings

derived, Hall	C₁₃×C₄₃ ⋊ C₂×C₉
Hall	C₁₃×C₄₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₄₃ ⋊ C₉
Sylow	C₄₃ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₄₃⋊C₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₃×C₄₃⋊C₃
commutator, hypocenter	C₁₃×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₄₃	C₂×C₃
prime radical	C₃×D₁₃×C₄₃	C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

408 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₄₃⋊C₉)⋊#261, #261×C₄₃⋊C₉, D₁₃×D₄₃⋊C₉, …
maximal normal subgroup of	(C₄₃⋊C₉)⋊#261, #261×C₄₃⋊C₉, D₁₃×D₄₃⋊C₉, …
maximal quotient of	Dic₁₃×C₄₃⋊C₉, C₂×D₁₃×C₄₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10062, 17);