Finite Group Databasebeta

D17×#1601 #17006391

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD17×#1601

Splittings

FittingC17×#1601 ⋊ C2
SylowC17 ⋊ C2×#1601

Subgroups

subgroupG/H
centerC22#120×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#1601C2
socleC22×C17C2×#120
prime radicalD17×#534C2
hypercenter#1601D17
hypocenterC17C2×#1601
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1601

1652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 141635);