Finite Group Databasebeta

D13×#1707 #15850564

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct productD13×#1707

Splittings

FittingC13×#1707 ⋊ C2
SylowC13 ⋊ C2×#1707

Subgroups

subgroupG/H
centerC22D13×#127
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#1707C2
socleC22×C13C2×#127
prime radicalC22×D13#127
hypercenter#1707D13
hypocenterC13C2×#1707
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #1707

814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 157213);