Finite Group Databasebeta

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C2×D4×PSU(3,𝔽2)⋊C3 #72220107

order3456
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×D4×PSU(3,𝔽2)⋊C3

Splittings

FittingC2×C32×D4 ⋊ SL(2,𝔽3)

Subgroups

subgroupG/H
centerC22C22×PSU(3,𝔽2)⋊C3
commutator, cosocleC2×PSU(3,𝔽2)C23×C3
FrattiniC2C23×PSU(3,𝔽2)⋊C3
FittingC2×C32×D4SL(2,𝔽3)
socleC22×C32C22×SL(2,𝔽3)
hypercenterC2×D4PSU(3,𝔽2)⋊C3
hypocenterPSU(3,𝔽2)C2×C3×D4
LCSG ▷ C2×PSU(3,𝔽2) ▷ PSU(3,𝔽2)
UCSC1 ◁ C22 ◁ C2×D4

1296 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 135 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 ofC2×D4×AGL(2,𝔽3), AGL(1,ℤ/8)×PSU(3,𝔽2)⋊C3, #72220199, …
maximal normal subgroup ofC2×D4×AGL(2,𝔽3), AGL(1,ℤ/8)×PSU(3,𝔽2)⋊C3, #72220199, …
maximal quotient ofAGL(1,ℤ/8)×PSU(3,𝔽2)⋊C3, #120×PSU(3,𝔽2)⋊C3, #127×PSU(3,𝔽2)⋊C3, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.