Finite Group DatabasebetaFinite Group Databasebeta| order | 31098 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D73⋊C3 |
| unambiguous semidirect product | D73⋊(C3×C71) |
| unambiguous semidirect product | (C73⋊C3)⋊(C2×C71) |
| unambiguous semidirect product | (C71×D73)⋊C3 |
| Fitting, socle, Hall | C71×C73 ⋊ C2×C3 |
| derived, Sylow | C73 ⋊ C2×C3×C71 |
| Hall | C71×C73⋊C3 ⋊ C2 |
| Hall | C71×D73 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C2×C71 |
| Hall | D73 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C2×C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C71×C73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5183 |
1278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31098, 10);