Finite Group Databasebeta

D17×#1898 #17036101

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD17×#1898

Splittings

FittingC17×#1898 ⋊ C2
SylowC17 ⋊ C2×#1898

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#1898C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#120×D17C2
cosocleC24×C17C24
hypercenter#1898D17
hypocenterC17C2×#1898
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ #1898

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 171345);