Finite Group Databasebeta

C22×#11763690 #17968227

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11763690

Splittings

SylowC17 ⋊ C22×#344

Subgroups

subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#95
prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C22×#344
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103471);