Finite Group DatabasebetaFinite Group Databasebeta| order | 31220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×D223 |
| unambiguous semidirect product | (D7×C223)⋊(C2×C5) |
| unambiguous semidirect product | (C7×D223)⋊(C2×C5) |
| unambiguous semidirect product | D1561⋊(C2×C5) |
| Fitting, socle, Hall | C5×C7×C223 ⋊ C22 |
| derived, Hall | C7×C223 ⋊ C22×C5 |
| Hall | C5×C223 ⋊ C2×D7 |
| Sylow | C223 ⋊ C2×C5×D7 |
| Hall | C5×C7 ⋊ C2×D223 |
| Sylow | C7 ⋊ C2×C5×D223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×D223 |
| commutator, cosocle, hypocenter | C7×C223 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C223 | C22 |
| LCS | G ▷ C7×C223 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7805 |
2825 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31220, 10);