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C32×C4×AGL(1,ℤ/9) #14518886

order1944
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C33

Aliases

direct productC32×C4×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C33×C4)
unambiguous semidirect product(C4×D9)⋊C33
unambiguous semidirect product(C3×C4×D9)⋊C32

Splittings

FittingC32×C4×3−1+2 ⋊ C2
derivedC9 ⋊ C2×C33×C4
SylowC32×3−1+2 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC32×C4AGL(1,ℤ/9)
commutator, hypocenterC9C2×C33×C4
FrattiniC2×C3C2×C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C2×C3×D3
prime radicalC2×C32×AGL(1,ℤ/9)C2
cosocleC2×C9C22×C33
LCSG ▷ C9
UCSC1 ◁ C32×C4

978 conjugacy classes of subgroups; only the 326 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 326 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

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3280);