Finite Group Databasebeta

← Prev (#40998234) Next (#40998236) →

C11×#14559022 #40998235

order26598
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#14559022

Splittings

Fitting, socle, HallC11×C13×C31 ⋊ C2×C3
derived, HallC13×C31 ⋊ C2×C3×C11
HallC11×#11925882 ⋊ C2
HallC11×C13×D31 ⋊ C3
Hall#11925882 ⋊ C2×C11
HallC13×D31 ⋊ C3×C11
HallC11×D31 ⋊ C13⋊C3
HallC11×C31 ⋊ C2×C13⋊C3
HallC11×C13 ⋊ D31⋊C3
HallD31 ⋊ C11×C13⋊C3
SylowC31 ⋊ C2×C11×C13⋊C3
SylowC13 ⋊ C11×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#14559022
commutator, cosocle, hypocenterC13×C31C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C31C2×C3
LCSG ▷ C13×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4433

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26598, 23);