Finite Group Databasebeta

D13×#3136 #16732149

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productD13×#3136

Splittings

FittingC13×#3136 ⋊ C2
SylowC13 ⋊ C2×#3136

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3136C2
socleC22×C13C23×D4
prime radicalD13×#535C2
hypercenter#3136D13
hypocenterC13C2×#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #3136

2262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1038798);