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C2×C4×AGL(2,𝔽3) #72217955

order3456
isoclinismisoclinic class of AGL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×AGL(2,𝔽3)

Splittings

FittingC2×C32×C4 ⋊ GL(2,𝔽3)
derivedPSU(3,𝔽2)⋊C3 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4AGL(2,𝔽3)
commutator, hypocenterPSU(3,𝔽2)⋊C3C22×C4
FrattiniC2C22×AGL(2,𝔽3)
FittingC2×C32×C4GL(2,𝔽3)
socleC22×C32C2×GL(2,𝔽3)
prime radicalC22×AGL(2,𝔽3)C2
cosocleC2×PSU(3,𝔽2)⋊C3C23
LCSG ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C2×C4

1056 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 70 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

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×AGL(2,𝔽3), C2×C3×C4×AGL(2,𝔽3), C2×D4×AGL(2,𝔽3), …
maximal normal subgroup ofC2×C3×C4×AGL(2,𝔽3), C2×D4×AGL(2,𝔽3), M16×AGL(2,𝔽3), …
maximal quotient ofC2×AGL(1,𝔽5)×AGL(2,𝔽3), C2×C3×C4×AGL(2,𝔽3), M16×AGL(2,𝔽3), …
automorphism group ofC3⋊(C3⋊C16), C5×C3⋊Dic3, C2×C5×C3⋊D3

GAP

Past the SmallGroups library coverage — no SmallGroups id.