Finite Group Databasebeta

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C3×D5×PSU(3,𝔽2) #72217336

order2160
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×D5×PSU(3,𝔽2)

Splittings

Fitting, socle, HallC33×C5 ⋊ C2×Q8
SylowC33 ⋊ Q8×D5
SylowC5 ⋊ C2×C3×PSU(3,𝔽2)

Subgroups

subgroupG/H
center, hypercenterC3D5×PSU(3,𝔽2)
commutator, cosocleC5×C3⋊D3C23×C3
FrattiniC1G
Fitting, socleC33×C5C2×Q8
prime radicalC3×D5×C3⋊D3C22
hypocenterC32×C5C2×C3×Q8
LCSG ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1 ◁ C3

180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×AΓL(1,𝔽9), C3×D5×PSU(3,𝔽2)⋊C3, C3×AGL(1,𝔽5)×PSU(3,𝔽2), …
maximal normal subgroup ofC3×D5×AΓL(1,𝔽9), C3×D5×PSU(3,𝔽2)⋊C3, C3×AGL(1,𝔽5)×PSU(3,𝔽2), …
maximal quotient ofC2×C3×D5×PSU(3,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.