Finite Group Databasebeta

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C22⋊C4×PSU(3,𝔽2)⋊C3 #72220406

order3456
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC22⋊C4×PSU(3,𝔽2)⋊C3

Splittings

FittingC32×C22⋊C4 ⋊ SL(2,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC22C22×PSU(3,𝔽2)⋊C3
commutatorC2×PSU(3,𝔽2)C2×C3×C4
FittingC32×C22⋊C4SL(2,𝔽3)
socleC22×C32C22×SL(2,𝔽3)
prime radicalC23×PSU(3,𝔽2)⋊C3C2
cosocleC22×PSU(3,𝔽2)C22×C3
hypercenterC22⋊C4PSU(3,𝔽2)⋊C3
hypocenterPSU(3,𝔽2)C3×C22⋊C4
LCSG ▷ C2×PSU(3,𝔽2) ▷ PSU(3,𝔽2)
UCSC1 ◁ C22 ◁ C22⋊C4

716 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 71 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

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#120×PSU(3,𝔽2)⋊C3, C22⋊C4×AGL(2,𝔽3), #72220447, …
maximal normal subgroup of#120×PSU(3,𝔽2)⋊C3, C22⋊C4×AGL(2,𝔽3), #72220447, …
maximal quotient of#104×PSU(3,𝔽2)⋊C3, #99×PSU(3,𝔽2)⋊C3, #100×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.