Finite Group Databasebeta

D13×#2139 #16015813

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

Aliases

direct productD13×#2139

Splittings

FittingC13×#2139 ⋊ C2
SylowC13 ⋊ C2×#2139

Subgroups

subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2139C2
socleC22×C13C22×D8
prime radicalC2×D13×#135C2
cosocleC2×C8×C13C24
hypercenter#2139D13
hypocenterC13C2×#2139
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322462);