Finite Group Databasebeta

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C3×#10591320 #13158238

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

Aliases

direct productC3×#10591320

Splittings

SylowC33 ⋊ #390

Subgroups

subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×C4⋊(C3⋊D3)C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#390
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

1522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 24301);