Finite Group Databasebeta

← Prev (#44538103) Next (#44538105) →

C2×C121×D65 #44538104

order31460
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C121×D65
unambiguous semidirect product(C2×C5)⋊(D13×C121)
unambiguous semidirect product(C2×C13)⋊(D5×C121)

Splittings

FittingC2×C5×C13×C121 ⋊ C2
derived, HallC5×C13 ⋊ C22×C121
HallC5×C13×C121 ⋊ C22
HallC13×C121 ⋊ C2×D5
HallC5×C121 ⋊ C2×D13
SylowC13 ⋊ C2×D5×C121
SylowC5 ⋊ C2×D13×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D65
commutator, hypocenterC5×C13C22×C121
FrattiniC11C2×C11×D65
FittingC2×C5×C13×C121C2
socleC2×C5×C11×C13C2×C11
prime radicalC2×C11×D65C11
cosocleC5×C11×C13C22×C11
LCSG ▷ C5×C13
UCSC1 ◁ C2×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15730

Conjugacy classes & character table

8228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 44);