Finite Group Databasebeta

← Prev (#44538066) Next (#44538068) →

C5×C13×Dic121 #44538067

order31460
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic121

Splittings

derived, SylowC121 ⋊ C4×C5×C13
HallC5×C13×C121 ⋊ C4
HallC13×C121 ⋊ C4×C5
HallC5×C121 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D121
commutator, hypocenterC121C4×C5×C13
FrattiniC2×C11C5×C13×D11
FittingC2×C5×C13×C121C2
socle, prime radicalC2×C5×C11×C13D11
cosocleC2×C121C2×C5×C13
LCSG ▷ C121
UCSC1 ◁ C2×C5×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31460

Conjugacy classes & character table

8060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 7);