Finite Group Databasebeta

C22×#11762727 #17200511

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11762727

Splittings

FittingC22×C17×#95 ⋊ C2
SylowC17 ⋊ C22×#394

Subgroups

subgroupG/H
centerC25C22×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×#95C2
socleC25×C17C23
prime radicalC24×D68C2
hypercenterC22×#95D17
hypocenterC17C22×#394
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C25 ◁ C22×#95

8798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 335755);