Finite Group Databasebeta

C2×#13129109 #16770216

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#13129109

Splittings

FittingC2×C13×H(3,𝔽4) ⋊ C2
SylowC13 ⋊ C2×#3540

Subgroups

subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×H(3,𝔽4)C2
socleC23×C13C25
hypercenterC2×H(3,𝔽4)D13
hypocenterC13C2×#3540
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

7418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076865);