Finite Group Databasebeta

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C2×D4×AGL(2,𝔽3) #72220161

order6912
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×AGL(2,𝔽3)

Splittings

FittingC2×C32×D4 ⋊ GL(2,𝔽3)

Subgroups

subgroupG/H
centerC22C22×AGL(2,𝔽3)
commutator, cosocleC2×PSU(3,𝔽2)⋊C3C24
FrattiniC2C23×AGL(2,𝔽3)
FittingC2×C32×D4GL(2,𝔽3)
socleC22×C32C22×GL(2,𝔽3)
hypercenterC2×D4AGL(2,𝔽3)
hypocenterPSU(3,𝔽2)⋊C3C22×D4
LCSG ▷ C2×PSU(3,𝔽2)⋊C3 ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C22 ◁ C2×D4

5996 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 5996 conjugacy classes of subgroups — too many to draw. Only its 194 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), #127×AGL(2,𝔽3), #120×AGL(2,𝔽3), …
maximal normal subgroup ofAGL(1,ℤ/8)×AGL(2,𝔽3), #127×AGL(2,𝔽3), #120×AGL(2,𝔽3), …
maximal quotient ofAGL(1,ℤ/8)×AGL(2,𝔽3), #127×AGL(2,𝔽3), #120×AGL(2,𝔽3)
automorphism group of#3744, C2×C3⋊(C3⋊C8), #3748, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.