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C32×C22⋊H(3,𝔽3) #11758109

order972
isoclinismisoclinic class of C9⋊A4
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C2×C37

Aliases

direct productC32×C22⋊H(3,𝔽3)

Splittings

FittingC22×C34 ⋊ C3
SylowC22 ⋊ C32×H(3,𝔽3)

Subgroups

subgroupG/H
centerC33C3×A4
commutator, cosocleC22×C3C34
FrattiniC3C33×A4
FittingC22×C34C3
socleC22×C33C32
hypercenterC34A4
hypocenterC22C32×H(3,𝔽3)
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C33 ◁ C34

1112 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

derived subgroup ofC3⋊(C3⋊#6258)
maximal subgroup ofC32×(C3⋊S4)⋊C3, C32×#6258, C3×C3⋊((C3⋊S4)⋊C3), …
maximal normal subgroup ofC32×(C3⋊S4)⋊C3, C32×#6258, C3×C3⋊((C3⋊S4)⋊C3), …
maximal quotient ofC32×Q8⋊H(3,𝔽3), C2×C32×C22⋊H(3,𝔽3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 834);