Finite Group Databasebeta

C3×D9×C4⋊C8 #13142013

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×D9×C4⋊C8

Splittings

FittingC3×C9×C4⋊C8 ⋊ C2
SylowC3×C9 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C22×D9
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×C4⋊C8C2
socleC22×C32C2×C4×D3
prime radicalC22×C3×D9C2×C4
cosocleC2×C4×C9C23×C3
hypercenterC3×C4⋊C8D9
hypocenterC9C2×C3×C4⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×C4⋊C8

452 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, 8076);