Finite Group Databasebeta

C2×#13131283 #16807471

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13131283
unambiguous semidirect productD13⋊#2283

Splittings

FittingC22×C42×C13 ⋊ C4
SylowC13 ⋊ C2×#2283

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C42×C13C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C42#261
hypocenterC13C2×#2283
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42

3246 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, 1114120);