Finite Group Databasebeta

← Prev (#44527822) Next (#44527824) →

C3×C7×#13093361 #44527823

order31122
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×#13093361

Splittings

Fitting, socleC3×C7×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C32×C7
HallC3×C7×#10625203 ⋊ C2
HallC7×C13×D19 ⋊ C32
HallC3×#10625203 ⋊ C2×C7
HallC7×C13×C19 ⋊ C2×C32
HallC13×D19 ⋊ C32×C7
HallC7×D19 ⋊ C3×C13⋊C3
HallC7×C19 ⋊ C2×C3×C13⋊C3
HallC7×C13 ⋊ C3×D19⋊C3
HallD19 ⋊ C3×C7×C13⋊C3
SylowC19 ⋊ C2×C3×C7×C13⋊C3
SylowC13 ⋊ C3×C7×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7#13093361
commutator, cosocle, hypocenterC13×C19C2×C32×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 306);