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C3×A4×H(3,𝔽3) #11758100

order972
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C2×C37

Aliases

direct productC3×A4×H(3,𝔽3)

Splittings

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

Subgroups

subgroupG/H
centerC32C32×A4
commutator, cosocleC22×C3C34
FrattiniC3C33×A4
FittingC22×C3×H(3,𝔽3)C3
socleC22×C32C33
hypercenterC3×H(3,𝔽3)A4
hypocenterC22C32×H(3,𝔽3)
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3⋊(A4⋊#272), #72259823
maximal subgroup ofC3×S4×H(3,𝔽3), H(3,𝔽3)×C3⋊S4, C3×A4⋊((C3⋊D3)⋊C3), …
maximal normal subgroup ofC3×S4×H(3,𝔽3), H(3,𝔽3)×C3⋊S4, C3×A4⋊((C3⋊D3)⋊C3), …
maximal quotient ofC3×SL(2,𝔽3)×H(3,𝔽3), C2×C3×A4×H(3,𝔽3), C3×A4×AΣL(1,𝔽27), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 825);