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C2×Q8×3−1+2⋊C4 #13153668

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×3−1+2⋊C4

Splittings

Sylow3−1+2 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×AGL(1,ℤ/9)
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC22×Q8×3−1+2C2
socleC23×C3C22×C3×D3
prime radicalC23×C32C22×D3
cosocleC22×C9C24×C3
hypercenterC22×Q8AGL(1,ℤ/9)
hypocenterC9C2×C3×C4×Q8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×Q8

972 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19731);