Finite Group Databasebeta

← Prev (#11757779) Next (#11757781) →

A₄×C₉⋊C₉ #11757780

order	972
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₂×C₃³

Aliases

A₄×C₉⋊C₉

Splittings

Fitting	C₂²×C₉⋊C₉ ⋊ C₃
Sylow	C₂² ⋊ C₃×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×A₄
commutator	C₂²×C₃	C₃²×C₉
Fitting	C₂²×C₉⋊C₉	C₃
socle, cosocle	C₂²×C₃²	C₃³
prime radical	C₃²×A₄	C₃²
hypercenter	C₉⋊C₉	A₄
hypocenter	C₂²	C₃×C₉⋊C₉
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 324

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	S₄×C₉⋊C₉, A₄⋊(D₉⋊C₉), A₄×D₉⋊C₉, …
maximal normal subgroup of	S₄×C₉⋊C₉, A₄⋊(D₉⋊C₉), A₄×D₉⋊C₉, …
maximal quotient of	SL(2,𝔽₃)×C₉⋊C₉, C₂×A₄×C₉⋊C₉, A₄×#6875, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 505);