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C2×Q16×AGL(1,ℤ/9) #13153467

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

Aliases

direct productC2×Q16×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C2×C3×Q16)
unambiguous semidirect product(C2×Q16×D9)⋊C3

Splittings

FittingC2×Q16×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC22D4×AGL(1,ℤ/9)
commutator, cosocleC4×C9C24×C3
FrattiniC3×C4C23×C3×D3
FittingC2×Q16×3−1+2C2
socleC22×C3C3×D3×D4
prime radicalC22×AGL(1,ℤ/9)D4
hypercenterC2×Q16AGL(1,ℤ/9)
hypocenterC9C22×C3×Q16
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19530);