Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×Dic14 |
| Hall | C7×H(3,𝔽3) ⋊ Q8 |
| Sylow | C7 ⋊ Q8×H(3,𝔽3) |
132 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)(10,11,12,13)(14,17,16,15)(18,19,20,21,22,23,24);(2,5,6)(4,8,9)(10,14,12,16)(11,15,13,17)(19,24)(20,23)(21,22)187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 342);