Finite Group Databasebeta

C2×D17×#431 #17898027

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×D17×#431

Splittings

FittingC2×C17×#431 ⋊ C2
SylowC17 ⋊ C22×#431

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC2×C17×#431C2
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC2×C4×C17C25
hypercenterC2×#431D17
hypocenterC17C22×#431
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×#431

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033271);