Finite Group Databasebeta

C2×#13113262 #15829314

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

Aliases

direct productC2×#13113262

Splittings

FittingC2×C13×#431 ⋊ C2
SylowC13 ⋊ C2×#1486

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#431C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D52C4
cosocleC42×C13C24
hypercenterC2×#431D13
hypocenterC13C2×#1486
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

1714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135963);