Finite Group Databasebeta

D17×#3069 #17901732

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD17×#3069

Splittings

FittingC17×#3069 ⋊ C2
SylowC17 ⋊ C2×#3069

Subgroups

subgroupG/H
centerC2C2×#121×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#3069C2
socleC2×C17C22×#121
prime radicalD17×#575C2
hypercenter#3069D17
hypocenterC17C2×#3069
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3069

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036976);