Finite Group Databasebeta

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C₅×C₂²⋊C₉×C₄₁ #20301563

order	7380
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₅×C₉×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₂²⋊C₉×C₄₁
unambiguous semidirect product	C₂²⋊(C₅×C₉×C₄₁)
unambiguous semidirect product	(C₂²×C₅)⋊(C₉×C₄₁)
unambiguous semidirect product	(C₂²×C₅×C₄₁)⋊C₉

Splittings

derived, Sylow	C₂² ⋊ C₅×C₉×C₄₁
Hall	C₂²×C₅×C₄₁ ⋊ C₉
Hall	C₂²×C₄₁ ⋊ C₅×C₉
Hall	C₂²×C₅ ⋊ C₉×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅×C₄₁	A₄
commutator, hypocenter	C₂²	C₅×C₉×C₄₁
Frattini	C₃	C₅×A₄×C₄₁
Fitting, socle	C₂²×C₃×C₅×C₄₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₄₁

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²⋊C₉×C₄₁⋊C₂₅, C₂₅×C₂²⋊C₉×C₄₁, C₅×C₂²⋊C₉×C₄₁⋊C₅, …
maximal normal subgroup of	C₂²⋊C₉×C₄₁⋊C₂₅, C₂₅×C₂²⋊C₉×C₄₁, C₅×C₂²⋊C₉×C₄₁⋊C₅, …
maximal quotient of	C₂₅×C₂²⋊C₉×C₄₁, C₅²×C₂²⋊C₉×C₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 41);