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C2×#63476⋊C3 #13153451

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

Aliases

direct productC2×#63476⋊C3
unambiguous semidirect product(C2×#63476)⋊C3

Splittings

FittingC2×SD16×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C2×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22D4×AGL(1,ℤ/9)
commutator, cosocleC4×C9C24×C3
FrattiniC3×C4C23×C3×D3
FittingC2×SD16×3−1+2C2
socleC22×C3C3×D3×D4
hypercenterC2×SD16AGL(1,ℤ/9)
hypocenterC9C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/8)×AGL(1,ℤ/9), #72244690, #72244757
maximal normal subgroup ofC2×AGL(1,ℤ/8)×AGL(1,ℤ/9), #72244690, #72244757
maximal quotient of#72244690, #72252816, #72252824

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19514);