Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#21439056 |
| Fitting, Hall | C4×C7×C361 ⋊ C3 |
| derived, Hall | C7×C361 ⋊ C3×C4 |
| Hall | C4×C361 ⋊ ΓL(1,𝔽8) |
| Sylow | C361 ⋊ C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C361⋊C3 |
| Sylow | C7 ⋊ C4×C361⋊C3 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10108 |
3380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 17);