Finite Group Databasebeta

C2×#13116527 #16015757

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

Aliases

direct productC2×#13116527

Splittings

FittingC2×C13×#413 ⋊ C2
SylowC13 ⋊ C2×#2134

Subgroups

subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C23×C4
FrattiniC2×Q8C23×D13
FittingC2×C13×#413C2
socleC22×C13C2×#99
prime radicalC2×#11719535C2
cosocleC2×Q8×C13C24
hypercenterC2×#413D13
hypocenterC13C2×#2134
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322406);