Finite Group Databasebeta

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C3×C4×C5×PSU(3,𝔽2) #72219426

order4320
isoclinismisoclinic class of PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×C4×C5×PSU(3,𝔽2)

Splittings

FittingC33×C4×C5 ⋊ Q8
HallC33×C5 ⋊ C4×Q8
SylowC33 ⋊ C4×C5×Q8

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5PSU(3,𝔽2)
commutatorC3⋊D3C22×C3×C4×C5
FrattiniC2C2×C3×C5×PSU(3,𝔽2)
FittingC33×C4×C5Q8
socleC2×C33×C5C2×Q8
prime radicalC2×C3×C5×C3⋊D3C23
cosocleC2×C3⋊D3C23×C3×C5
hypocenterC32C3×C4×C5×Q8
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C3×C4×C5

324 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 140 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

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

Relationships

maximal subgroup ofC3×C4×C5×PSU(3,𝔽2)⋊C3, C3×C4×C5×AΓL(1,𝔽9)
maximal normal subgroup ofC3×C4×C5×PSU(3,𝔽2)⋊C3, C3×C4×C5×AΓL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.