Finite Group Databasebeta

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M16×AGL(2,𝔽3) #72220165

order6912
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productM16×AGL(2,𝔽3)

Splittings

FittingC32×M16 ⋊ GL(2,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC4C22×AGL(2,𝔽3)
commutatorC2×PSU(3,𝔽2)⋊C3C22×C4
FittingC32×M16GL(2,𝔽3)
socleC2×C32C2×C4×GL(2,𝔽3)
prime radicalC22×AGL(2,𝔽3)C4
cosocleC4×PSU(3,𝔽2)⋊C3C23
hypercenterM16AGL(2,𝔽3)
hypocenterPSU(3,𝔽2)⋊C3C2×M16
LCSG ▷ C2×PSU(3,𝔽2)⋊C3 ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C4 ◁ M16

1348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 78 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

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×AGL(2,𝔽3)
maximal normal subgroup ofAGL(1,ℤ/8)×AGL(2,𝔽3)
maximal quotient of#97×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.