Finite Group Databasebeta

D17×#1691 #17016841

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

Aliases

direct productD17×#1691

Splittings

FittingC17×#1691 ⋊ C2
SylowC17 ⋊ C2×#1691

Subgroups

subgroupG/H
centerC22#121×D17
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#1691C2
socleC22×C17C2×#121
prime radicalC2×D4×D17D4
hypercenter#1691D17
hypocenterC17C2×#1691
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #1691

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 152085);