Finite Group Databasebeta

C22×#11763705 #17978186

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11763705

Splittings

SylowC17 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C23×C8
FrattiniC2×C4C23×#595
FittingC24×C4×C17C4
socleC23×C17C22⋊C8
prime radicalC25×C17C8
cosocleC2×#3622C24
hypercenterC24×C4#595
hypocenterC17C22×#349
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113430);