Finite Group Databasebeta

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C2×C4×D3×3−1+2 #13048842

order1296
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D3×3−1+2
unambiguous semidirect product(C2×C4×D3×C9)⋊C3

Splittings

FittingC2×C3×C4×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C22×C4

Subgroups

subgroupG/H
centerC2×C3×C4C32×D3
commutatorC32C22×C32×C4
FrattiniC2×C3C22×C32×D3
FittingC2×C3×C4×3−1+2C2
socleC22×C32C22×C32
prime radicalC22×C32×D3C2×C3
cosocleC2×C32C23×C32
hypercenterC2×C4×3−1+2D3
hypocenterC3C22×C4×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C4×3−1+2

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×D3×AGL(1,ℤ/9), C2×D3×D4×3−1+2, C2×D3×C4⋊AGL(1,ℤ/9)
maximal normal subgroup ofC2×C4×D3×AGL(1,ℤ/9), C2×D3×D4×3−1+2, C2×D3×C4⋊AGL(1,ℤ/9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2560);