Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C11 |
| direct product | C3×ΓL(1,𝔽8)×C11⋊Dic11 |
| unambiguous semidirect product | C11⋊(C3×ΓL(1,𝔽8)×Dic11) |
| derived, Hall | C7×C112 ⋊ C32×C4 |
| Hall | C3×C112×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×C11⋊Dic11 ⋊ C32 |
| Sylow | C112 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×C11⋊Dic11 |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10164 |
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 233);