Finite Group Databasebeta

D17×#1904 #17036202

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD17×#1904

Splittings

FittingC17×#1904 ⋊ C2
SylowC17 ⋊ C2×#1904

Subgroups

subgroupG/H
centerC2D17×#386
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1904C2
socleC2×C17C2×#386
prime radicalC2×AGL(1,ℤ/8)×D17C2
cosocleC22×C4×C17C24
hypercenter#1904D17
hypocenterC17C2×#1904
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1904

1894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171446);