Finite Group Databasebeta

D17×#1564 #17003294

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productD17×#1564

Splittings

FittingC17×#1564 ⋊ C2
SylowC17 ⋊ C2×#1564

Subgroups

subgroupG/H
centerC42D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC17×#1564C2
socleC22×C17C22×C4⋊C4
prime radicalC23×D17C4⋊C4
cosocleC42×C17C24
hypercenter#1564D17
hypocenterC17C2×#1564
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1564

830 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, 138538);