Finite Group Databasebeta

← Prev (#13048897) Next (#13048899) →

C2×C4×C3⋊AGL(1,ℤ/9) #13048898

order1296
isoclinismisoclinic class of C3⋊AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C4×C3⋊AGL(1,ℤ/9)

Splittings

FittingC2×C3×C4×3−1+2 ⋊ C2
derivedC3×C9 ⋊ C22×C3×C4
SylowC3×3−1+2 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊AGL(1,ℤ/9)
commutator, hypocenterC3×C9C22×C3×C4
FrattiniC2×C3C22×C3×C3⋊D3
FittingC2×C3×C4×3−1+2C2
socleC22×C32C2×C3×D3
prime radicalC22×C3⋊AGL(1,ℤ/9)C2
cosocleC2×C3×C9C23×C3
LCSG ▷ C3×C9
UCSC1 ◁ C2×C4

612 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 216

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×#92314, C2×D4×C3⋊AGL(1,ℤ/9), #72219893, …
maximal normal subgroup ofC2×D4×C3⋊AGL(1,ℤ/9), #72219893, C42×C3⋊AGL(1,ℤ/9), …
maximal quotient ofC2×C4×#92314, C42×C3⋊AGL(1,ℤ/9), C22⋊C4×C3⋊AGL(1,ℤ/9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2616);