Finite Group Databasebeta

D17×#2956 #17898631

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD17×#2956

Splittings

FittingC17×#2956 ⋊ C2
SylowC17 ⋊ C2×#2956

Subgroups

subgroupG/H
centerC4C22×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC17×#2956C2
socleC2×C17C22×C4×D4
prime radicalD17×#575C2
cosocleC2×C4×C17C25
hypercenter#2956D17
hypocenterC17C2×#2956
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×M16 ◁ #2956

2674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 1033875);