Finite Group Databasebeta

D17×#1704 #17016992

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

Aliases

direct productD17×#1704

Splittings

FittingC17×#1704 ⋊ C2
SylowC17 ⋊ C2×#1704

Subgroups

subgroupG/H
centerC22#121×D17
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#1704C2
socleC22×C17C2×#121
prime radicalC22×D17#121
hypercenter#1704D17
hypocenterC17C2×#1704
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #1704

618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 152236);