Finite Group Databasebeta

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C32×#65780 #72231635

order2880
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3×C4

Aliases

direct productC32×#65780

Splittings

FittingC2×C32×C5×D4 ⋊ C4
HallC32×C5 ⋊ #390
SylowC5 ⋊ C32×#390

Subgroups

subgroupG/H
centerC22×C32C22×AGL(1,𝔽5)
commutatorC22×C5C22×C32×C4
FrattiniC22C22×C32×AGL(1,𝔽5)
FittingC2×C32×C5×D4C4
socleC22×C32×C5C22×C4
prime radicalC2×C32×D4×D5C2
cosocleC22×D5C23×C32
hypercenterC2×C32×D4AGL(1,𝔽5)
hypocenterC5C32×#390
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C2×C32×D4

1548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×#65780, C32×AGL(1,𝔽5)×#127, #72231689
maximal normal subgroup ofC3⋊D3×#65780, C32×AGL(1,𝔽5)×#127, #72231689

GAP

Past the SmallGroups library coverage — no SmallGroups id.