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C32×#1094 #11758108

order972
isoclinismisoclinic class of C9⋊A4
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C2×C35

Aliases

direct productC32×#1094

Splittings

SylowC22 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC33C3×A4
commutator, cosocleC22×C3C34
FrattiniC3C33×A4
Fitting, prime radicalC22×C34C3
socleC22×C33C32
hypercenterC34A4
hypocenterC22C32×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C33 ◁ C34

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×((C22⋊C9)⋊C2)⋊C3, C3×C3⋊(((C22⋊C9)⋊C2)⋊C3), C3⋊(C3⋊(((C22⋊C9)⋊C2)⋊C3)), …
maximal normal subgroup ofC32×((C22⋊C9)⋊C2)⋊C3, C3×C3⋊(((C22⋊C9)⋊C2)⋊C3), C3⋊(C3⋊(((C22⋊C9)⋊C2)⋊C3)), …
maximal quotient ofC32×#6204, C2×C32×#1094, 3−1+2×#1094, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 833);