Finite Group Databasebeta

C2×#13116002 #15890318

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116002

Splittings

SylowC13 ⋊ C2×#2030

Subgroups

subgroupG/H
centerC23#88207
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC2×C13×#543C2
socleC23×C13#120
prime radicalC25×C13C23
hypercenterC2×#543D13
hypocenterC13C2×#2030
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#543

1482 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 291 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, 196967);