Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C13×C121 ⋊ C22×C5 |
| Hall | C13×C121⋊C5 ⋊ C22 |
| Hall | D13×D121 ⋊ C5 |
| Hall | C121⋊C5 ⋊ C2×D13 |
| Sylow | C121 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ C2×D121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C121 | C22×C5 |
| Frattini | C11 | D13×AGL(1,𝔽11) |
| socle | C11×C13 | C2×AGL(1,𝔽11) |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 15);