Finite Group Databasebeta

D17×#1540 #17002609

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD17×#1540

Splittings

FittingC17×#1540 ⋊ C2
SylowC17 ⋊ C2×#1540

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC17×#1540C2
socleC22×C17C22×C22⋊C4
prime radicalD17×#532C2
cosocleC42×C17C24
hypercenter#1540D17
hypocenterC17C2×#1540
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 137853);