Finite Group Databasebeta

D17×#2120 #17187041

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD17×#2120

Splittings

FittingC17×#2120 ⋊ C2
SylowC17 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC4#99×D17
commutatorC23×C17C23×C4
FrattiniC2×D4C23×D17
FittingC17×#2120C2
socleC2×C17C22×#99
prime radicalD17×#525C2
cosocleC2×D4×C17C24
hypercenter#2120D17
hypocenterC17C2×#2120
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2120

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 322285);