Finite Group Databasebeta

D17×#2112 #17186990

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD17×#2112

Splittings

FittingC17×#2112 ⋊ C2
SylowC17 ⋊ C2×#2112

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D17
commutator, socleC22×C17C23×C8
FittingC17×#2112C2
prime radicalC24×D17C8
cosocleC2×C8×C17C24
hypercenter#2112D17
hypocenterC17C2×#2112
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ #2112

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322234);