Finite Group Databasebeta

← Prev (#13049294) Next (#13049296) →

C2×A4×AGL(1,ℤ/9) #13049295

order1296
isoclinismisoclinic class of A4×AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×A4×AGL(1,ℤ/9)
unambiguous semidirect product(D9⋊A4)⋊(C2×C3)
unambiguous semidirect product(C2×D9⋊A4)⋊C3
unambiguous semidirect product(C2×A4×D9)⋊C3
unambiguous semidirect product(C23×AGL(1,ℤ/9))⋊C3

Splittings

FittingC23×3−1+2 ⋊ C2×C3
derivedC22×C9 ⋊ C22×C32

Subgroups

subgroupG/H
center, hypercenterC2A4×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC22×C9C22×C32
FrattiniC3C2×C3×D3×A4
FittingC23×3−1+2C2×C3
socleC23×C3C32×D3
LCSG ▷ C22×C9
UCSC1 ◁ C2

338 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#997, C2×S4×AGL(1,ℤ/9), C22×A4×AGL(1,ℤ/9), …
maximal normal subgroup ofC2×S4×AGL(1,ℤ/9), C22×A4×AGL(1,ℤ/9), C4×A4×AGL(1,ℤ/9), …
maximal quotient ofC22×A4×AGL(1,ℤ/9), C2×SL(2,𝔽3)×AGL(1,ℤ/9), D5×A4×AGL(1,ℤ/9), …
automorphism group of#88614, D9⋊SL(2,𝔽3), Dic9⋊A4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 3013);