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C₄₇×D₁₃⋊C₉ #24926953

order	10998
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₄₇)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₄₇)
unambiguous semidirect product	(D₁₃×C₄₇)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₄₇
Hall	C₄₇×C₁₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₄₇ ⋊ C₉
Hall	C₁₃×C₄₇ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₄₇
Hall	D₁₃ ⋊ C₉×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₄₇
Frattini	C₃	C₄₇×D₁₃⋊C₃
Fitting, socle	C₃×C₁₃×C₄₇	C₂×C₃
prime radical	C₃×D₁₃×C₄₇	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₄₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1128 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#261⋊C₉, C₄₇⋊(#261⋊C₉), D₄₇×D₁₃⋊C₉, …
maximal normal subgroup of	C₄₇×#261⋊C₉, C₄₇⋊(#261⋊C₉), D₄₇×D₁₃⋊C₉, …
maximal quotient of	C₄₇×Dic₁₃⋊C₉, C₂×C₄₇×D₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10998, 11);