Finite Group Databasebeta

C22×#11719171 #16807465

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C213

Aliases

direct productC22×#11719171
unambiguous semidirect productD13⋊(C2×#379)

Splittings

FittingC26×C13 ⋊ C4
SylowC13 ⋊ C22×#379

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC26×C13C4
socleC24×C13C22×C4
prime radicalC26×D13C2
cosocleC22×D13C25
hypercenterC26#261
hypocenterC13C22×#379
LCSG ▷ C22×C13 ▷ C13
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) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114114);