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C2×#63502⋊C3 #13153621

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#63502⋊C3
unambiguous semidirect product(C2×#63502)⋊C3

Splittings

FittingC22×D4×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C2×#127

Subgroups

subgroupG/H
centerC23C22×AGL(1,ℤ/9)
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC22×D4×3−1+2C2
socleC23×C3C22×C3×D3
hypercenterC22×D4AGL(1,ℤ/9)
hypocenterC9C2×C3×#127
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×D4

1612 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#127×AGL(1,ℤ/9), C2×#10588922⋊C3, C2×#10588879⋊C3, …
maximal normal subgroup ofC2×#127×AGL(1,ℤ/9), C2×#10588922⋊C3, C2×#10588879⋊C3, …
maximal quotient of#72244711, #72244722, #72244777

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19684);