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C2×C3⋊(3−1+2⋊C4) #10619979

order648
isoclinismisoclinic class of C3⋊AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊(3−1+2⋊C4)
unambiguous semidirect product(C2×C3)⋊(3−1+2⋊C4)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22C3⋊AGL(1,ℤ/9)
commutator, hypocenterC3×C9C2×C3×C4
FrattiniC2×C3C2×C3×C3⋊D3
FittingC22×C3×3−1+2C2
socleC22×C32C3×D3
prime radicalC22×C33D3
cosocleC2×C3×C9C22×C3
LCSG ▷ C3×C9
UCSC1 ◁ C22

205 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×3−1+2⋊C4, (3−1+2⋊C4)⋊Dic3, #88442⋊C3, …
maximal normal subgroup ofDic3×3−1+2⋊C4, (3−1+2⋊C4)⋊Dic3, #88442⋊C3, …
maximal quotient ofC2×C3⋊(3−1+2⋊C8), #13047945, C4×C3⋊(3−1+2⋊C4), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 498);