Finite Group Databasebeta

C3×C4×Q8×D9 #13152677

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

Aliases

direct productC3×C4×Q8×D9

Splittings

FittingC3×C4×Q8×C9 ⋊ C2
SylowC3×C9 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C3×C4C22×D9
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC3×C4×Q8×C9C2
socleC22×C32C23×D3
prime radicalC22×C3×D9C23
cosocleC22×C9C24×C3
hypercenterC3×C4×Q8D9
hypocenterC9C2×C3×C4×Q8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×Q8

964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18740);