Finite Group Databasebeta

D13×#3037 #16729752

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD13×#3037

Splittings

FittingC13×#3037 ⋊ C2
SylowC13 ⋊ C2×#3037

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3037C2
socleC22×C13C23×D4
prime radicalD13×#532C2
hypercenter#3037D13
hypocenterC13C2×#3037
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

2810 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, 1036401);