Finite Group Databasebeta

D17×#2048 #17062150

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

Aliases

direct productD17×#2048

Splittings

FittingC17×#2048 ⋊ C2
SylowC17 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC2D17×#394
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2048C2
socleC2×C17C2×#394
prime radicalC2×AGL(1,ℤ/8)×D17C2
hypercenter#2048D17
hypocenterC17C2×#2048
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2048

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 197394);