Finite Group DatabasebetaFinite Group Databasebeta| order | 31005 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C53 · Schur multiplier (H2) = C1 |
| derived, Sylow | C13 ⋊ C5×C9×C53 |
| Hall | C5×C13×C53 ⋊ C9 |
| Hall | C13×C53 ⋊ C5×C9 |
| Hall | C5×C13 ⋊ C9×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C53 | C13⋊C3 |
| commutator, hypocenter | C13 | C5×C9×C53 |
| Frattini | C3 | C5×C13⋊C3×C53 |
| Fitting, socle, prime radical | C3×C5×C13×C53 | C3 |
| cosocle | C3×C13 | C3×C5×C53 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C5×C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31005 |
5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31005, 3);