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C3×C5×#3777 #72219422

order2160
isoclinismisoclinic class of PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×#3777

Splittings

HallC33×C5 ⋊ C4⋊C4
SylowC33 ⋊ C5×C4⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5PSU(3,𝔽2)
commutatorC3⋊D3C2×C3×C4×C5
FrattiniC2C3×C5×PSU(3,𝔽2)
Fitting, socleC2×C33×C5Q8
prime radicalC2×C3×C5×C3⋊D3C22
cosocleC2×C3⋊D3C22×C3×C5
hypocenterC32C3×C5×C4⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3×C5

132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 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 ofC3×C4×C5×PSU(3,𝔽2), C3×C5×GO+(4,𝔽2)⋊C4, C3×C5×AGL(1,𝔽9)⋊C4, …
maximal normal subgroup ofC3×C4×C5×PSU(3,𝔽2), C3×C5×GO+(4,𝔽2)⋊C4, C3×C5×AGL(1,𝔽9)⋊C4, …
maximal quotient ofC2×C3×C5×#3777

GAP

Past the SmallGroups library coverage — no SmallGroups id.