Finite Group Databasebeta

D17×#1659 #17015441

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productD17×#1659

Splittings

FittingC17×#1659 ⋊ C2
SylowC17 ⋊ C2×#1659

Subgroups

subgroupG/H
centerC22#120×D17
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#1659C2
socleC22×C17C2×#120
prime radicalD17×H(3,𝔽4)C2
hypercenter#1659D17
hypocenterC17C2×#1659
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #1659

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 150685);