Finite Group Databasebeta

C2×#13112972 #15783104

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13112972

Splittings

SylowC13 ⋊ C2×#1398

Subgroups

subgroupG/H
centerC2×C8C4×Dic13
commutatorC4×C13C2×C4×C8
FrattiniC2×C16C22×D13
FittingC2×C13×#346C2
socleC22×C13#346
prime radicalC23×C13M32
cosocleC2×C13×C16C23
hypercenterC2×#346D13
hypocenterC13C2×#1398
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×#346

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89753);