Finite Group Databasebeta

D13×#3131 #16732117

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

Aliases

direct productD13×#3131

Splittings

FittingC13×#3131 ⋊ C2
SylowC13 ⋊ C2×#3131

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3131C2
socleC22×C13C23×D4
prime radicalD13×#532C2
hypercenter#3131D13
hypocenterC13C2×#3131
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

2222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1038766);