Finite Group Databasebeta

C3×#10587479 #13108751

order1632
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#10587479

Splittings

HallC3×C17 ⋊ #106
SylowC17 ⋊ C3×#106

Subgroups

subgroupG/H
centerC22×C3C22⋊D17
commutatorC4×C17C2×C3×C4
FrattiniC2×C4C2×C3×D17
FittingC3×C4⋊C4×C17C2
socle, prime radicalC22×C3×C17D4
cosocleC2×C4×C17C22×C3
hypercenterC3×C4⋊C4D17
hypocenterC17C3×#106
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1632

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 86);