Finite Group Databasebeta

D17×#2064 #17062860

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

Aliases

direct productD17×#2064

Splittings

FittingC17×#2064 ⋊ C2
SylowC17 ⋊ C2×#2064

Subgroups

subgroupG/H
centerC22#121×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2064C2
socleC22×C17C2×#121
prime radicalC23×D17#41
hypercenter#2064D17
hypocenterC17C2×#2064
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2064

1006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 198104);