Finite Group Databasebeta

C2×#13129623 #16776768

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#13129623

Splittings

FittingC22×C13×2−1+4 ⋊ C2
SylowC13 ⋊ C2×#3586

Subgroups

subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC4×C13C26
FrattiniC4C25×D13
FittingC22×C13×2−1+4C2
socleC22×C13C23×D4
hypercenterC22×2−1+4D13
hypocenterC13C2×#3586
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×2−1+4

10794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1083417);