Finite Group Databasebeta

C22×#11762670 #17192586

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11762670

Splittings

SylowC17 ⋊ C22×#381

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC23×C22⋊C4×C17C2
socleC25×C17C23
prime radicalC26×C17C22
cosocleC23×C17C25
hypercenterC23×C22⋊C4D17
hypocenterC17C22×#381
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C22⋊C4

8062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327830);