Finite Group Databasebeta

C22×#11719061 #16807470

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11719061
unambiguous semidirect productD13⋊(C2×#383)

Splittings

FittingC22×C42×C13 ⋊ C4
SylowC13 ⋊ C22×#383

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C42×C13C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C42#261
hypocenterC13C22×#383
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42

3678 conjugacy classes of subgroups; only the 1168 normal subgroups are shown.

normal subgroups only

This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1168 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) = 832

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, 1114119);