Finite Group Databasebeta

C3×#10588649 #13142544

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10588649

Splittings

FittingC2×C3×C9×C4⋊C4 ⋊ C2
SylowC3×C9 ⋊ #417

Subgroups

subgroupG/H
centerC22×C3C2×#611
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C9×C4⋊C4C2
socleC22×C32C2×#67
prime radicalC2×C3×#3697C2
cosocleC2×C4×C9C23×C3
hypercenterC2×C3×C4⋊C4D9
hypocenterC9C3×#417
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8607);