Finite Group Databasebeta

C2×#13126661 #16739259

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13126661

Splittings

FittingC2×C8×D4×C13 ⋊ C2
SylowC13 ⋊ C2×#3295

Subgroups

subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C8×D4×C13C2
socleC23×C13C22×D4
prime radicalC2×D4×D52C2
hypercenterC2×C8×D4D13
hypocenterC13C2×#3295
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

2642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1045908);