Finite Group Databasebeta

C22×#11763750 #17978870

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C213

Aliases

direct productC22×#11763750
unambiguous semidirect productD17⋊(C2×#379)

Splittings

FittingC26×C17 ⋊ C4
SylowC17 ⋊ C22×#379

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC26×C17C4
socleC24×C17C22×C4
prime radicalC26×D17C2
cosocleC22×D17C25
hypercenterC26#595
hypocenterC17C22×#379
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C26

33214 conjugacy classes of subgroups; only the 2056 normal subgroups are shown.

normal subgroups only

This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 2056 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114114);