Finite Group DatabasebetaFinite Group Databasebeta| order | 31407 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#11762245 |
| Fitting, socle, Hall | C192×C29 ⋊ C3 |
| derived, Sylow | C192 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #11762245 |
| commutator, cosocle, hypocenter | C192 | C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C192×C29 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C29 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10469 |
3567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31407, 5);