Finite Group Databasebeta

Q8×C3⋊(C9⋊C8) #13144424

order1728
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3

Aliases

direct productQ8×C3⋊(C9⋊C8)

Splittings

SylowC3×C9 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊D9
commutatorC2×C3×C9C22×C8
FrattiniC2×C3×C4C22×C3⋊D3
FittingC3×C4×Q8×C9C2
socle, prime radicalC22×C32C22×Dic3
cosocleC2×C3×C4×C9C23
hypercenterC4×Q8C3⋊D9
hypocenterC3×C9C8×Q8
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C4×Q8

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1728

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10487);