Finite Group Databasebeta

D17×#1790 #17033581

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD17×#1790

Splittings

FittingC17×#1790 ⋊ C2
SylowC17 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC22#120×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#1790C2
socleC22×C17C2×#120
prime radicalC2×H(5,𝔽2)×D17C2
cosocleC24×C17C24
hypercenter#1790D17
hypocenterC17C2×#1790
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #1790

4402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 168825);