Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C23 |
| direct product | #217×#1094 |
3020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 24 points:
(6,8)(10,11,12)(13,14,15)(16,22,23,18,17,24,21,19,20);(1,2,3,4)(5,6)(7,8)(9,12)(10,11)(14,15)(17,19,22)(20,24,23)360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72245336 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((6,8)(10,11,12)(13,14,15)(16,22,23,18,17,24,21,19,20), (1,2,3,4)(5,6)(7,8)(9,12)(10,11)(14,15)(17,19,22)(20,24,23));