Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D183 |
| unambiguous semidirect product | (C3×D41)⋊D61 |
| unambiguous semidirect product | (C61×D41)⋊D3 |
| Fitting, socle, derived, Hall | C3×C41×C61 ⋊ C22 |
| Hall | C41×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D41 |
| Hall | C3×C41 ⋊ C2×D61 |
| Sylow | C61 ⋊ D3×D41 |
| Sylow | C41 ⋊ C2×D183 |
| Sylow | C3 ⋊ D41×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C41×C61 | C22 |
| LCS | G ▷ C3×C41×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7503 |
2046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 40);