Finite Group Databasebeta

C22×#11762739 #17200535

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11762739

Splittings

SylowC17 ⋊ C22×#398

Subgroups

subgroupG/H
centerC25C22×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC23×C4⋊C4×C17C2
socle, prime radicalC25×C17C23
hypercenterC23×C4⋊C4D17
hypocenterC17C22×#398
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C25 ◁ C23×C4⋊C4

4158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 335779);