Finite Group Databasebeta

C2×#14529326 #17036335

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

Aliases

direct productC2×#14529326

Splittings

FittingC2×C17×#518 ⋊ C2
SylowC17 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#11762688
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#518C2
socleC22×C17#386
prime radicalC2×#11763368C2
cosocleC24×C17C24
hypercenterC2×#518D17
hypocenterC17C2×#1913
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ C2×#518

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171579);