Finite Group Databasebeta

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C22×C3⋊D3×AGL(1,ℤ/8) #72243269

order2304
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214×C3

Aliases

direct productC22×C3⋊D3×AGL(1,ℤ/8)

Splittings

FittingC22×C32×AGL(1,ℤ/8) ⋊ C2
SylowC32 ⋊ C23×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC23C2×D4×C3⋊D3
commutator, cosocleC32×C4C26
FrattiniC4C25×C3⋊D3
FittingC22×C32×AGL(1,ℤ/8)C2
socleC23×C32C22×D4
hypercenterC22×AGL(1,ℤ/8)C3⋊D3
hypocenterC32C23×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

39930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.