Finite Group DatabasebetaFinite Group Databasebeta| order | 31220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C223⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C223⋊(C7×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C7×C223 ⋊ C4 |
| derived, Hall | C5×C223 ⋊ C4×C7 |
| Hall | C7×C223 ⋊ AGL(1,𝔽5) |
| Sylow | C223 ⋊ C7×AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ Dic223 |
| Sylow | C5 ⋊ C7×Dic223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C223⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C223 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C223 | C4 |
| prime radical | C7×D5×C223 | C2 |
| cosocle | D5×C223 | C2×C7 |
| LCS | G ▷ C5×C223 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7805 |
3143 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31220, 12);