Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C23 |
| direct product | D5×(C23⋊D23)⋊C3 |
| unambiguous semidirect product | (D5×C23⋊D23)⋊C3 |
| Fitting, socle, derived, Hall | C5×C232 ⋊ C22×C3 |
| Hall | D5×C23⋊D23 ⋊ C3 |
| Hall | C5×C232⋊C3 ⋊ C22 |
| Hall | C232⋊C3 ⋊ C2×D5 |
| Sylow | C232 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×(C23⋊D23)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C232 | C22×C3 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 345 |
376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 57);