Finite Group DatabasebetaFinite Group Databasebeta| order | 31220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1561 |
| unambiguous semidirect product | C7⋊(C5×Dic223) |
| unambiguous semidirect product | C223⋊(C5×Dic7) |
| derived, Hall | C7×C223 ⋊ C4×C5 |
| Hall | C5×C7×C223 ⋊ C4 |
| Hall | C5×C223 ⋊ Dic7 |
| Sylow | C223 ⋊ C5×Dic7 |
| Hall | C5×C7 ⋊ Dic223 |
| Sylow | C7 ⋊ C5×Dic223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1561 |
| commutator, hypocenter | C7×C223 | C4×C5 |
| Frattini | C2 | C5×D1561 |
| Fitting, socle, prime radical | C2×C5×C7×C223 | C2 |
| cosocle | C2×C7×C223 | C2×C5 |
| LCS | G ▷ C7×C223 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31220 |
7820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31220, 4);