Finite Group Databasebeta

C2×#13131072 #16806784

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

Aliases

direct productC2×#13131072

Splittings

SylowC13 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC22×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC22×C13×#41C4
socleC22×C13C2×C22⋊C8
cosocleC2×#1055C24
hypercenterC22×#41#261
hypocenterC13C2×#2115
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1113433);