Finite Group Databasebeta

C2×D3×C9×Q16 #13153459

order1728
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C25

Aliases

direct productC2×D3×C9×Q16

Splittings

FittingC2×C3×C9×Q16 ⋊ C2
SylowC3×C9 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC22×C9D3×D4
commutatorC3×C4C24×C9
FrattiniC3×C4C23×C3×D3
FittingC2×C3×C9×Q16C2
socleC22×C32C2×C3×D4
prime radicalC22×C3×D3C3×D4
cosocleC32×C4C24×C3
hypercenterC2×C9×Q16D3
hypocenterC3C22×C9×Q16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×C4×C9 ◁ C2×C9×Q16

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19522);