Finite Group Databasebeta

C2×#13130763 #16798184

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13130763

Splittings

SylowC13 ⋊ C2×#1839

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C42×C13C4
socle, prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC22×C42#261
hypocenterC13C2×#1839
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42

1134 conjugacy classes of subgroups; only the 432 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 432 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) = 3328

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, 1104833);