Finite Group Databasebeta

C2×#13116909 #16017296

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116909

Splittings

FittingC2×C13×#493 ⋊ C2
SylowC13 ⋊ C2×#2213

Subgroups

subgroupG/H
centerC22#11718733
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#493C2
socleC22×C13#459
hypercenterC2×#493D13
hypocenterC13C2×#2213
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#493

790 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, 323945);