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C₃×(C₃×A₄)⋊C₉ #11757827

order	972
isoclinism	isoclinic class of C₉⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₂×C₃⁴

Aliases

C₃×(C₃×A₄)⋊C₉

Splittings

Fitting	C₂²×C₃²×C₉ ⋊ C₃
Sylow	C₂² ⋊ C₃×C₃²⋊C₉

Subgroups

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 324

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₃⋊#10619754
maximal subgroup of	C₃×(C₃⋊S₄)⋊C₉, C₃×#10619754, C₃⋊((C₃⋊S₄)⋊C₉), …
maximal normal subgroup of	C₃×(C₃⋊S₄)⋊C₉, C₃×#10619754, C₃⋊((C₃⋊S₄)⋊C₉), …
maximal quotient of	C₃×(C₃×SL(2,𝔽₃))⋊C₉, C₂×C₃×(C₃×A₄)⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 552);