Finite Group Databasebeta

C2×#13123101 #16069331

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13123101

Splittings

FittingC2×C13×#399 ⋊ C2
SylowC13 ⋊ C2×#2842

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#399C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#399D13
hypocenterC13C2×#2842
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 375980);