Finite Group Databasebeta

D17×#1721 #17022101

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C8

Aliases

direct productD17×#1721

Splittings

FittingC17×#1721 ⋊ C2
SylowC17 ⋊ C2×#1721

Subgroups

subgroupG/H
centerC22#127×D17
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#1721C2
socleC22×C17C2×#127
hypercenter#1721D17
hypocenterC17C2×#1721
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #1721

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 157345);