Finite Group Databasebeta

D17×#1450 #16999900

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C8

Aliases

direct productD17×#1450

Splittings

FittingC17×#1450 ⋊ C2
SylowC17 ⋊ C2×#1450

Subgroups

subgroupG/H
centerC4×C8C22×D17
commutatorC2×C17C22×C4×C8
FrattiniC42C23×D17
FittingC17×#1450C2
socleC22×C17C22×C42
prime radicalC23×D17C42
cosocleC42×C17C24
hypercenter#1450D17
hypocenterC17C2×#1450
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C8 ◁ #1450

982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135144);