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C2×3−1+2×(C3⋊D3)⋊C3 #72254053

order2916
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33

Aliases

direct productC2×3−1+2×(C3⋊D3)⋊C3

Splittings

FittingC2×H(3,𝔽3)×3−1+2 ⋊ C2
SylowH(3,𝔽3)×3−1+2 ⋊ C22

Subgroups

subgroupG/H
centerC2×C3C32×(C3⋊D3)⋊C3
commutator, cosocleC33C22×C33
FrattiniC32C2×C33×D3
FittingC2×H(3,𝔽3)×3−1+2C2
socleC2×C32C33×D3
prime radicalC2×C32×(C3⋊D3)⋊C3C3
hypercenterC2×3−1+2(C3⋊D3)⋊C3
hypocenterC32C22×C3×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

1110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×3−1+2×(C3⋊D3)⋊C3, C2×(C3⋊D3)⋊C3×AGL(1,ℤ/9)
maximal normal subgroup ofC2×(C3⋊D3)⋊C3×AGL(1,ℤ/9)
maximal quotient ofD3×3−1+2×(C3⋊D3)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.