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Q8×C4⋊AGL(1,ℤ/9) #13152736

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

Aliases

direct productQ8×C4⋊AGL(1,ℤ/9)

Splittings

FittingC4×Q8×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ D4×Q8

Subgroups

subgroupG/H
centerC22C23×AGL(1,ℤ/9)
commutator, cosocleC22×C9C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC4×Q8×3−1+2C2
prime radicalC2×C4⋊AGL(1,ℤ/9)C22
hypercenterC4×Q8AGL(1,ℤ/9)
hypocenterC9C3×D4×Q8
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8

875 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18799);