Finite Group Databasebeta

D13×#2127 #16015700

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD13×#2127

Splittings

FittingC13×#2127 ⋊ C2
SylowC13 ⋊ C2×#2127

Subgroups

subgroupG/H
centerC2C2×D13×#99
commutatorC2×C4×C13C23×C4
FrattiniC2×D4C23×D13
FittingC13×#2127C2
socleC2×C13C22×#99
prime radicalD13×#535C2
cosocleC2×D4×C13C24
hypercenter#2127D13
hypocenterC13C2×#2127
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #2127

1510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322349);