Finite Group Databasebeta

D13×#2120 #16015636

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD13×#2120

Splittings

FittingC13×#2120 ⋊ C2
SylowC13 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC4D13×#99
commutatorC23×C13C23×C4
FrattiniC2×D4C23×D13
FittingC13×#2120C2
socleC2×C13C22×#99
prime radicalD13×#525C2
cosocleC2×D4×C13C24
hypercenter#2120D13
hypocenterC13C2×#2120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2120

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 322285);