Finite Group Databasebeta

D17×#2097 #17064109

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

Aliases

direct productD17×#2097

Splittings

FittingC17×#2097 ⋊ C2
SylowC17 ⋊ C2×#2097

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2097C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenter#2097D17
hypocenterC17C2×#2097
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 199353);