Finite Group Databasebeta

C22×#11763779 #17979438

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11763779

Splittings

SylowC17 ⋊ C22×#407

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
Fitting, prime radicalC26×C17C4
socleC24×C17C22×C4
cosocleC2×Dic17C25
hypercenterC26#595
hypocenterC17C22×#407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C26

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114682);