Finite Group Databasebeta

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C32×#65800 #72229951

order2880
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC32×#65800

Splittings

FittingC24×C32×C5 ⋊ C4
HallC32×C5 ⋊ #379
SylowC5 ⋊ C32×#379

Subgroups

subgroupG/H
centerC22×C32C22×AGL(1,𝔽5)
commutatorC22×C5C22×C32×C4
FrattiniC22C22×C32×AGL(1,𝔽5)
FittingC24×C32×C5C4
socleC22×C32×C5C22×C4
prime radicalC24×C32×D5C2
cosocleC22×D5C23×C32
hypercenterC24×C32AGL(1,𝔽5)
hypocenterC5C32×#379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C24×C32

3036 conjugacy classes of subgroups; only the 480 normal subgroups are shown.

normal subgroups only

This group has 3036 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) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC32×AGL(1,𝔽5)×#120, C3⋊D3×#65800, #72260159
maximal normal subgroup ofC32×AGL(1,𝔽5)×#120, C3⋊D3×#65800, #72260159

GAP

Past the SmallGroups library coverage — no SmallGroups id.