Finite Group Databasebeta

D17×#1390 #16949261

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1390

Splittings

FittingC17×#1390 ⋊ C2
SylowC17 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC22#99×D17
commutatorC23×C17C2×C42
FrattiniC22×D4C22×D17
FittingC17×#1390C2
socleC22×C17C2×#99
prime radicalC22×D4×D17C22
cosocleC22×D4×C17C23
hypercenter#1390D17
hypocenterC17C2×#1390
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84505);