Finite Group Databasebeta

D17×#2262 #17192448

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD17×#2262

Splittings

FittingC17×#2262 ⋊ C2
SylowC17 ⋊ C2×#2262

Subgroups

subgroupG/H
centerC4D16×D17
commutator, cosocleC16×C17C24
FrattiniC16C23×D17
FittingC17×#2262C2
socleC2×C17C22×D16
hypercenter#2262D17
hypocenterC17C2×#2262
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327692);