Finite Group Databasebeta

C3×#10587483 #13108755

order1632
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10587483

Splittings

HallC3×C17 ⋊ M32
SylowC17 ⋊ C3×M32

Subgroups

subgroupG/H
centerC3×C8C2×D17
commutatorC2×C17C2×C3×C8
FrattiniC8C2×C3×D17
FittingC2×C3×C8×C17C2
socleC2×C3×C17C2×C8
prime radicalC22×C3×C17C8
cosocleC8×C17C22×C3
hypercenterC2×C3×C8D17
hypocenterC17C3×M32
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 90);