Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#73105 |
3643 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);(9,11,13,20,14,21,12,19)(10,15,16,18,17,23,22,24);(6,7)(9,10,12,16,14,17,13,22)(11,18,19,23,21,24,20,15)176 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#73105 |
| maximal normal subgroup of | A4×#73105 |
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), (9,11,13,20,14,21,12,19)(10,15,16,18,17,23,22,24), (6,7)(9,10,12,16,14,17,13,22)(11,18,19,23,21,24,20,15));