Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C361 · Schur multiplier (H2) = C2 |
| direct product | C22⋊ΓL(1,𝔽8)×C361 |
| unambiguous semidirect product | C22⋊(ΓL(1,𝔽8)×C361) |
| unambiguous semidirect product | C7⋊(A4×C361) |
| Fitting, Hall | C22×C7×C361 ⋊ C3 |
| derived, Hall | C22×C7 ⋊ C3×C361 |
| Hall | C7×C361 ⋊ A4 |
| Hall | C22×C361 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×C361 |
| Sylow | C22 ⋊ ΓL(1,𝔽8)×C361 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10108 |
4332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 55);