Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×C7⋊C8 |
| Hall | C7×H(3,𝔽3) ⋊ C8 |
| Sylow | C7 ⋊ C8×H(3,𝔽3) |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4)(3,6,8)(5,9,7)(11,12)(13,14)(15,16)(17,18,19,21,20,22,23,24);(2,5,6)(4,8,9)(10,11,13,15,16,14,12)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 65);