Finite Group Databasebeta

D17×#3417 #17940845

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD17×#3417

Splittings

FittingC17×#3417 ⋊ C2
SylowC17 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC2C22×D8×D17
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC17×#3417C2
socleC2×C17C23×D8
hypercenter#3417D17
hypocenterC17C2×#3417
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ #41 ◁ #131 ◁ #3417

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076089);