Finite Group Databasebeta

D17×#1461 #17000128

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productD17×#1461

Splittings

FittingC17×#1461 ⋊ C2
SylowC17 ⋊ C2×#1461

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC17×#1461C2
socleC22×C17C22×C22⋊C4
prime radicalC23×D17C22×C4
cosocleC22×C4×C17C24
hypercenter#1461D17
hypocenterC17C2×#1461
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135372);