Finite Group Databasebeta

C2×#13113218 #15829271

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

Aliases

direct productC2×#13113218

Splittings

SylowC13 ⋊ C2×#1476

Subgroups

subgroupG/H
centerC2×C42C22⋊D13
commutatorC4×C13C23×C8
FrattiniC42C23×D13
FittingC2×C4×C13×#41C2
socleC23×C13C2×C22⋊C4
prime radicalC22×C13×#41C4
cosocleC42×C13C24
hypercenterC2×C4×#41D13
hypocenterC13C2×#1476
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×#41

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135920);