Finite Group DatabasebetaFinite Group Databasebeta| order | 31780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C227 · Schur multiplier (H2) = C2 |
| direct product | D5×D7×C227 |
| unambiguous semidirect product | (C7×D5)⋊(C2×C227) |
| unambiguous semidirect product | (C5×D7)⋊(C2×C227) |
| unambiguous semidirect product | D35⋊(C2×C227) |
| Fitting, socle, Hall | C5×C7×C227 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C22×C227 |
| Hall | C7×C227 ⋊ C2×D5 |
| Hall | C5×C227 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D5×C227 |
| Sylow | C5 ⋊ C2×D7×C227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C227 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C22×C227 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C227 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C227 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7945 |
4540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31780, 17);