Finite Group Databasebeta

C2×#14529327 #17036336

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529327

Splittings

SylowC17 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#11762689
commutatorC23×C17C23×C4
FrattiniC24C23×D17
Fitting, prime radicalC2×C17×#534C2
socleC22×C17#386
cosocleC24×C17C24
hypercenterC2×#534D17
hypocenterC17C2×#1913
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171580);