Finite Group Databasebeta

C2×#13130770 #16798256

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13130770

Splittings

SylowC13 ⋊ C2×#1843

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×#95C4
socle, prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#95#261
hypocenterC13C2×#1843
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#95

1230 conjugacy classes of subgroups; only the 456 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 456 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

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104905);