Finite Group Databasebeta

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C32×#65688 #72231622

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

Aliases

direct productC32×#65688

Splittings

FittingC32×C42×C5 ⋊ C4
HallC32×C5 ⋊ #384
SylowC5 ⋊ C32×#384

Subgroups

subgroupG/H
centerC22×C32C22×AGL(1,𝔽5)
commutatorC22×C5C22×C32×C4
FrattiniC22C22×C32×AGL(1,𝔽5)
FittingC32×C42×C5C4
socleC22×C32×C5C22×C4
prime radicalC22×C32×D5C23
cosocleC22×D5C23×C32
hypercenterC32×C42AGL(1,𝔽5)
hypocenterC5C32×#384
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C32×C42

1116 conjugacy classes of subgroups; only the 480 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 480 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×#65688, C32×AGL(1,𝔽5)×#127, #72231684
maximal normal subgroup ofC3⋊D3×#65688, C32×AGL(1,𝔽5)×#127, #72231684

GAP

Past the SmallGroups library coverage — no SmallGroups id.