Finite Group Databasebeta

C2×D17×#471 #17901693

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D17×#471

Splittings

FittingC2×C17×#471 ⋊ C2
SylowC17 ⋊ C22×#471

Subgroups

subgroupG/H
centerC22#121×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#471C2
socleC22×C17C2×#121
prime radicalC2×AGL(1,ℤ/8)×D17C2
hypercenterC2×#471D17
hypocenterC17C22×#471
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036937);