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C₅×C₂₄₁⋊C₉ #24925722

order	10845
automorphism	?
homology	Abelianization (H₁) = C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₄₁⋊C₉
unambiguous semidirect product	(C₅×C₂₄₁)⋊C₉

Splittings

derived, Sylow	C₂₄₁ ⋊ C₅×C₉
Hall	C₅×C₂₄₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅	C₂₄₁⋊C₃
commutator, hypocenter	C₂₄₁	C₅×C₉
Frattini	C₃	C₅×C₂₄₁⋊C₃
Fitting, socle, prime radical	C₃×C₅×C₂₄₁	C₃
cosocle	C₃×C₂₄₁	C₃×C₅
LCS	G ▷ C₂₄₁
UCS	C₁ ◁ C₃×C₅

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1245 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₂₄₁⋊C₉, C₅×D₂₄₁⋊C₉, D₅×C₂₄₁⋊C₉, …
maximal normal subgroup of	C₂×C₅×C₂₄₁⋊C₉, C₅×D₂₄₁⋊C₉, D₅×C₂₄₁⋊C₉, …
maximal quotient of	C₂×C₅×C₂₄₁⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10845, 4);