Finite Group Databasebeta

D17×SD16⋊C8 #17003705

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD17×SD16⋊C8

Splittings

FittingC17×SD16⋊C8 ⋊ C2
SylowC17 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC17×SD16⋊C8C2
socleC22×C17C2×C4×D4
prime radicalC2×D4×D17C2×C4
cosocleC42×C17C24
hypercenterSD16⋊C8D17
hypocenterC17C2×SD16⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

806 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, 138949);