Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×#73104 |
3051 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 24 points:
(3,4)(5,6,8);(1,2);(1,2)(3,4)(10,14)(15,20)(16,21)(22,24);(6,7)(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24)224 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#73104 |
| maximal normal subgroup of | A4×#73104 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4)(5,6,8), (1,2), (1,2)(3,4)(10,14)(15,20)(16,21)(22,24), (6,7)(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24));