Finite Group Databasebeta

← Prev (#72217490) Next (#72217492) →

C2×C3×C5×PSU(3,𝔽2) #72217491

order2160
isoclinismisoclinic class of PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×C3×C5×PSU(3,𝔽2)

Splittings

Fitting, socleC2×C33×C5 ⋊ Q8
HallC33×C5 ⋊ C2×Q8
SylowC33 ⋊ C2×C5×Q8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5PSU(3,𝔽2)
commutator, cosocleC3⋊D3C23×C3×C5
FrattiniC1G
Fitting, socleC2×C33×C5Q8
prime radicalC2×C3×C5×C3⋊D3C22
hypocenterC32C2×C3×C5×Q8
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3×C5

180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C5×PSU(3,𝔽2)⋊C3, C2×C3×D5×PSU(3,𝔽2), C2×C3×C5×AΓL(1,𝔽9), …
maximal normal subgroup ofC2×C3×C5×PSU(3,𝔽2)⋊C3, C2×C3×D5×PSU(3,𝔽2), C2×C3×C5×AΓL(1,𝔽9), …
maximal quotient ofC22×C3×C5×PSU(3,𝔽2), C3×C4×C5×PSU(3,𝔽2), C2×C3×C5×#3777

GAP

Past the SmallGroups library coverage — no SmallGroups id.