Finite Group Databasebeta

C2×#13116270 #15891745

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

Aliases

direct productC2×#13116270

Splittings

FittingC22×C13×#106 ⋊ C2
SylowC13 ⋊ C2×#2077

Subgroups

subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#106C2
socleC24×C13C2×D4
prime radicalC24×D13D4
hypercenterC22×#106D13
hypocenterC13C2×#2077
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 198394);