Finite Group Databasebeta

C22×#11763868 #17981022

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763868

Splittings

SylowC17 ⋊ C22×#504

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C24×C8
FrattiniC4C24×#595
FittingC22×M16×C17C4
socleC23×C17C22×C8
prime radicalC22×#63252C4
cosocle#3622C25
hypercenterC22×M16#595
hypocenterC17C22×#504
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×M16

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116266);