Finite Group Databasebeta

← Prev (#72218923) Next (#72218925) →

C3×C8×PSU(3,𝔽2)⋊C3 #72218924

order5184
isoclinismisoclinic class of PSU(3,𝔽2)⋊C3
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C32

Aliases

direct productC3×C8×PSU(3,𝔽2)⋊C3

Splittings

FittingC33×C8 ⋊ SL(2,𝔽3)
derivedPSU(3,𝔽2) ⋊ C32×C8

Subgroups

subgroupG/H
center, hypercenterC3×C8PSU(3,𝔽2)⋊C3
commutator, hypocenterPSU(3,𝔽2)C32×C8
FrattiniC4C2×C3×PSU(3,𝔽2)⋊C3
FittingC33×C8SL(2,𝔽3)
socleC2×C33C4×SL(2,𝔽3)
prime radicalC2×C3×PSU(3,𝔽2)⋊C3C4
cosocleC4×PSU(3,𝔽2)C2×C32
LCSG ▷ PSU(3,𝔽2)
UCSC1 ◁ C3×C8

358 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 54 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

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C16×PSU(3,𝔽2)⋊C3, C3×C8×AGL(2,𝔽3), C3×#72218959
maximal normal subgroup ofC3×C16×PSU(3,𝔽2)⋊C3, C3×C8×AGL(2,𝔽3), C3×#72218959
maximal quotient ofC3×C16×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.