Finite Group Databasebeta

D17×#2052 #17062195

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD17×#2052

Splittings

FittingC17×#2052 ⋊ C2
SylowC17 ⋊ C2×#2052

Subgroups

subgroupG/H
centerC22#121×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2052C2
socleC22×C17C2×#121
prime radicalC2×#41×D17C22
hypercenter#2052D17
hypocenterC17C2×#2052
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2052

1362 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, 197439);