Finite Group Databasebeta

C2×#13131064 #16806767

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13131064

Splittings

SylowC13 ⋊ C2×#2112

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C23×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socleC23×C13C22×C8
prime radicalC24×D13C8
cosocleC2×#1055C24
hypercenterC23×C8#261
hypocenterC13C2×#2112
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C8

1406 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, 1113416);