Finite Group Databasebeta

D17×#2227 #17188949

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

Aliases

direct productD17×#2227

Splittings

FittingC17×#2227 ⋊ C2
SylowC17 ⋊ C2×#2227

Subgroups

subgroupG/H
centerC22C2×D8×D17
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#2227C2
socleC22×C17C22×D8
prime radicalC22×D17C2×D8
hypercenter#2227D17
hypocenterC17C2×#2227
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 324193);