Finite Group Databasebeta

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D5×D13×C121 #44538093

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

Aliases

direct productD5×D13×C121
unambiguous semidirect product(D5×C13)⋊(C2×C121)
unambiguous semidirect product(C5×D13)⋊(C2×C121)
unambiguous semidirect productD65⋊(C2×C121)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC121D5×D13
commutator, hypocenterC5×C13C22×C121
FrattiniC11D5×C11×D13
FittingC5×C13×C121C22
socle, cosocleC5×C11×C13C22×C11
prime radicalD5×C11×D13C11
LCSG ▷ C5×C13
UCSC1 ◁ C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7865

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 33);