Finite Group Databasebeta

← Prev (#40998226) Next (#40998228) →

C11×C31×D39 #40998227

order26598
automorphism?
homologyAbelianization (H1) = C2×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC11×C31×D39
unambiguous semidirect productC3⋊(C11×D13×C31)
unambiguous semidirect productC13⋊(D3×C11×C31)

Splittings

Fitting, socle, HallC3×C11×C13×C31 ⋊ C2
derived, HallC3×C13 ⋊ C2×C11×C31
HallC11×C13×C31 ⋊ D3
HallC3×C13×C31 ⋊ C2×C11
HallC3×C11×C31 ⋊ D13
HallC3×C11×C13 ⋊ C2×C31
HallC13×C31 ⋊ D3×C11
HallC11×C13 ⋊ D3×C31
HallC3×C31 ⋊ C11×D13
HallC3×C11 ⋊ D13×C31
SylowC13 ⋊ D3×C11×C31
SylowC3 ⋊ C11×D13×C31

Subgroups

subgroupG/H
center, hypercenterC11×C31D39
commutator, cosocle, hypocenterC3×C13C2×C11×C31
FrattiniC1G
Fitting, socleC3×C11×C13×C31C2
LCSG ▷ C3×C13
UCSC1 ◁ C11×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13299

Conjugacy classes & character table

7161 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26598, 15);