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C₃×#66353 #11757815

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

Aliases

Splittings

C₂² ⋊ C₃×C₂₇⋊C₃

Subgroups

170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 162

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×((C₂²⋊C₂₇)⋊C₂)⋊C₃, C₃⋊(((C₂²⋊C₂₇)⋊C₂)⋊C₃), D₃×#66353, …
maximal normal subgroup of	C₃×((C₂²⋊C₂₇)⋊C₂)⋊C₃, C₃⋊(((C₂²⋊C₂₇)⋊C₂)⋊C₃), D₃×#66353, …
maximal quotient of	C₃×#10619570, C₂×C₃×#66353

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 540);