Finite Group DatabasebetaFinite Group Databasebeta| order | 31098 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D71×C73⋊C3 |
| unambiguous semidirect product | C71⋊(C2×C73⋊C3) |
| unambiguous semidirect product | (C73×D71)⋊C3 |
| Fitting, socle, derived, Hall | C71×C73 ⋊ C2×C3 |
| Hall | C71×C73⋊C3 ⋊ C2 |
| Hall | C73×D71 ⋊ C3 |
| Sylow | C73 ⋊ C3×D71 |
| Sylow | C71 ⋊ C2×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C71×C73 | C2×C3 |
| LCS | G ▷ C71×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5183 |
999 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31098, 11);