Finite Group Databasebeta

D17×#1749 #17031844

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productD17×#1749

Splittings

FittingC17×#1749 ⋊ C2
SylowC17 ⋊ C2×#1749

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D17
commutatorC22×C17C22×C42
FittingC17×#1749C2
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenter#1749D17
hypocenterC17C2×#1749
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1749

2286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167088);