Finite Group Databasebeta

D17×#1637 #17010041

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1637

Splittings

FittingC17×#1637 ⋊ C2
SylowC17 ⋊ C2×#1637

Subgroups

subgroupG/H
centerC22#120×D17
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#1637C2
socleC22×C17C2×#120
prime radicalC2×D4×D17D4
hypercenter#1637D17
hypocenterC17C2×#1637
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #1637

1174 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, 145285);