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C8×3−1+2⋊Q8 #13141465

order1728
isoclinismisoclinic class of 3−1+2⋊Q8
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×3−1+2⋊Q8
unambiguous semidirect product(C8×Dic18)⋊C3

Splittings

Sylow3−1+2 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×AGL(1,ℤ/9)
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC4×C8×3−1+2C2
socleC22×C3C2×C3×C4×D3
prime radicalC22×C32C2×C4×D3
cosocleC2×C4×C9C23×C3
hypercenterC4×C8AGL(1,ℤ/9)
hypocenterC9C3×C8×Q8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C8 ◁ C4×C8

328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7528);