Finite Group Databasebeta

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C2×C3×C3⋊D3×AGL(1,ℤ/8) #72269002

order3456
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C3

Aliases

direct productC2×C3×C3⋊D3×AGL(1,ℤ/8)

Splittings

FittingC2×C33×AGL(1,ℤ/8) ⋊ C2
SylowC33 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22×C3C2×D4×C3⋊D3
commutator, cosocleC32×C4C25×C3
FrattiniC4C24×C3×C3⋊D3
FittingC2×C33×AGL(1,ℤ/8)C2
socleC22×C33C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)C3⋊D3
hypocenterC32C22×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

11512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.