Finite Group DatabasebetaFinite Group Databasebeta| order | 31115 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×C127⋊C49 |
| unambiguous semidirect product | C127⋊(C5×C49) |
| unambiguous semidirect product | (C5×C127)⋊C49 |
| derived, Sylow | C127 ⋊ C5×C49 |
| Hall | C5×C127 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C127⋊C7 |
| commutator, hypocenter | C127 | C5×C49 |
| Frattini | C7 | C5×C127⋊C7 |
| Fitting, socle, prime radical | C5×C7×C127 | C7 |
| cosocle | C7×C127 | C5×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C5×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31115 |
875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31115, 2);