Finite Group Databasebeta

C3×#10587500 #13108772

order1632
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10587500

Splittings

HallC3×C17 ⋊ Q32
SylowC17 ⋊ C3×Q32

Subgroups

subgroupG/H
centerC2×C3#63228
commutator, cosocleC8×C17C22×C3
FrattiniC8C2×C3×D17
FittingC3×Q16×C17C2
socle, prime radicalC2×C3×C17D8
hypercenterC3×Q16D17
hypocenterC17C3×Q32
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 1632

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 107);