Finite Group Databasebeta

C2×#13130564 #16796877

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13130564

Splittings

FittingC2×C13×C22⋊C8 ⋊ C4
SylowC13 ⋊ C2×#1749

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C13×C22⋊C8C4
socleC23×C13C2×C42
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC2×C22⋊C8#261
hypocenterC13C2×#1749
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

2286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103526);