Finite Group DatabasebetaFinite Group Databasebeta| order | 31220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D223 |
| unambiguous semidirect product | D1115⋊D7 |
| unambiguous semidirect product | D1561⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C223 ⋊ C22 |
| Hall | C7×C223 ⋊ C2×D5 |
| Hall | C5×C223 ⋊ C2×D7 |
| Sylow | C223 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D223 |
| Sylow | C7 ⋊ D5×D223 |
| Sylow | C5 ⋊ D7×D223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C223 | C22 |
| LCS | G ▷ C5×C7×C223 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7805 |
Polycyclic presentation:
2^2,5,7,223|d^a=d^6,e^a=e^222,c^b=c^4,d^b=d^62129 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31220, 20);