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C22×C3⋊(3−1+2⋊C4) #13048945

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

Aliases

direct productC22×C3⋊(3−1+2⋊C4)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC23C3⋊AGL(1,ℤ/9)
commutator, hypocenterC3×C9C22×C3×C4
FrattiniC2×C3C22×C3×C3⋊D3
FittingC23×C3×3−1+2C2
socleC23×C32C3×D3
prime radicalC23×C33D3
cosocleC2×C3×C9C23×C3
LCSG ▷ C3×C9
UCSC1 ◁ C23

684 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 278 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) = 432

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×C3⋊(3−1+2⋊C4), C22×C4×C3⋊AGL(1,ℤ/9), #72254746, …
maximal normal subgroup ofD4×C3⋊(3−1+2⋊C4), C22×C4×C3⋊AGL(1,ℤ/9), #72254746, …
maximal quotient ofD4×C3⋊(3−1+2⋊C4), C22×#11757618, C22×C3⋊(#1094⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2663);