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C₃³×C₂²⋊C₉ #11758107

order	972
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃³×C₉ · Schur multiplier (H₂) = C₂×C₃⁶

Aliases

C₃³×C₂²⋊C₉

Splittings

C₂² ⋊ C₃³×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃⁴	A₄
commutator, hypocenter	C₂²	C₃³×C₉
Frattini	C₃	C₃³×A₄
Fitting, socle, prime radical	C₂²×C₃⁴	C₃
cosocle	C₂²×C₃	C₃⁴
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃⁴

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 486

Conjugacy classes & character table

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

Relationships

derived subgroup of	C₃⋊(C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂)))
maximal subgroup of	C₃³×(C₂²⋊C₉)⋊C₂, C₃²×C₃⋊((C₂²⋊C₉)⋊C₂), C₃×C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂)), …
maximal normal subgroup of	C₃³×(C₂²⋊C₉)⋊C₂, C₃²×C₃⋊((C₂²⋊C₉)⋊C₂), C₃×C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂)), …
maximal quotient of	C₃³×Q₈⋊C₉, C₂×C₃³×C₂²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 832);