Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×ΓL(1,𝔽8)⋊Dic7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic7×C53) |
| derived, Sylow | C72 ⋊ C3×C4×C53 |
| Hall | C53×C7⋊Dic7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C53 ⋊ C4 |
| Hall | C72×C53 ⋊ C3×C4 |
| Hall | C7⋊Dic7 ⋊ C3×C53 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C4×C53 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4452 |
2332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 53);