Finite Group Databasebeta

C2×#13130508 #16796764

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13130508

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C22×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C2×C4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC22×C13C2×#95
prime radicalC24×D13D4
cosocleC2×C4×D13C24
hypercenterC22×M16#261
hypocenterC13C22×H(3,ℤ/4)
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103413);