Finite Group Databasebeta

D17×#1280 #16923910

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1280

Splittings

FittingC17×#1280 ⋊ C2
SylowC17 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C17C2×C4×C8
FrattiniC23×C4C22×D17
FittingC17×#1280C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×C4×C17C23
hypercenter#1280D17
hypocenterC17C2×#1280
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59154);