Finite Group Databasebeta

← Prev (#72277270) Next (#72277272) →

C2×D3×D8×AGL(1,𝔽5) #72277271

order3840
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D3×D8×AGL(1,𝔽5)

Splittings

FittingC2×C3×C5×D8 ⋊ C2×C4
HallC3×C5 ⋊ C22×C4×D8
SylowC5 ⋊ C2×C4×D3×D8
SylowC3 ⋊ C22×D8×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC22D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C24×C4
FrattiniC4C23×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D8C2×C4
socleC22×C3×C5C2×C4×D4
prime radicalC2×D3×D5×D8C2
cosocleC3×C4×D5C25
hypercenterC2×D8D3×AGL(1,𝔽5)
hypocenterC3×C5C22×C4×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

7388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.