Finite Group Databasebeta

D17×#2238 #17189205

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

Aliases

direct productD17×#2238

Splittings

FittingC17×#2238 ⋊ C2
SylowC17 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC2D17×#481
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#2238C2
socleC2×C17C2×#481
prime radicalD17×#469C2
hypercenter#2238D17
hypocenterC17C2×#2238
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2238

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 324449);