Finite Group Databasebeta

D17×#2077 #17063148

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

Aliases

direct productD17×#2077

Splittings

FittingC17×#2077 ⋊ C2
SylowC17 ⋊ C2×#2077

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2077C2
socleC23×C17C22×D4
prime radicalC24×D17D4
hypercenter#2077D17
hypocenterC17C2×#2077
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 198392);