Finite Group Databasebeta

D13×#1740 #15860348

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productD13×#1740

Splittings

FittingC13×#1740 ⋊ C2
SylowC13 ⋊ C2×#1740

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC13×#1740C2
socleC22×C13C22×C22⋊C4
prime radicalC24×D13C23
cosocleC24×C13C24
hypercenter#1740D13
hypocenterC13C2×#1740
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

2350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 166997);