Finite Group Databasebeta

C2×#13131073 #16806786

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

Aliases

direct productC2×#13131073

Splittings

SylowC13 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C8C22⋊#261
commutatorC22×C13C23×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×#6127C4
cosocleC2×#1055C24
hypercenterC23×C8#261
hypocenterC13C2×#2115
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113435);