Finite Group DatabasebetaFinite Group Databasebeta| order | 31970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×D139⋊C23 |
| unambiguous semidirect product | D139⋊(C5×C23) |
| unambiguous semidirect product | (C5×D139)⋊C23 |
| unambiguous semidirect product | (C139⋊C23)⋊(C2×C5) |
| Fitting, socle, Hall | C5×C139 ⋊ C2×C23 |
| derived, Sylow | C139 ⋊ C2×C5×C23 |
| Hall | C5×C139⋊C23 ⋊ C2 |
| Hall | C139⋊C23 ⋊ C2×C5 |
| Hall | C5×D139 ⋊ C23 |
| Hall | D139 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D139⋊C23 |
| commutator, cosocle, hypocenter | C139 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C139 | C2×C23 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 695 |
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31970, 10);