Finite Group Databasebeta

D17×#3230 #17906368

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD17×#3230

Splittings

FittingC17×#3230 ⋊ C2
SylowC17 ⋊ C2×#3230

Subgroups

subgroupG/H
centerC22C22×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#3230C2
socleC22×C17C23×D4
prime radicalC23×D17C2×D4
hypercenter#3230D17
hypocenterC17C2×#3230
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

2006 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, 1041612);