Finite Group Databasebeta

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C3×C4×AGL(2,𝔽3) #72217550

order5184
isoclinismisoclinic class of AGL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4×AGL(2,𝔽3)

Splittings

FittingC33×C4 ⋊ GL(2,𝔽3)
derivedPSU(3,𝔽2)⋊C3 ⋊ C2×C3×C4

Subgroups

subgroupG/H
center, hypercenterC3×C4AGL(2,𝔽3)
commutator, hypocenterPSU(3,𝔽2)⋊C3C2×C3×C4
FrattiniC2C2×C3×AGL(2,𝔽3)
FittingC33×C4GL(2,𝔽3)
socleC2×C33C2×GL(2,𝔽3)
prime radicalC2×C3×AGL(2,𝔽3)C2
cosocleC2×PSU(3,𝔽2)⋊C3C22×C3
LCSG ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C3×C4

579 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 579 conjugacy classes of subgroups — too many to draw. Only its 44 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

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×AGL(2,𝔽3), C2×C3×C4×AGL(2,𝔽3), C3×C8×AGL(2,𝔽3), …
maximal normal subgroup ofC2×C3×C4×AGL(2,𝔽3), C3×C8×AGL(2,𝔽3), C3×C4×C5×AGL(2,𝔽3)
maximal quotient ofC3×AGL(1,𝔽5)×AGL(2,𝔽3), C2×C3×C4×AGL(2,𝔽3), C3×C8×AGL(2,𝔽3), …
automorphism group ofC13×C3⋊D3

GAP

Past the SmallGroups library coverage — no SmallGroups id.