Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4700 |
| Fitting | C3×C4×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #443 |
| Sylow | C3 ⋊ C5×#443 |
212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,12,13,22,15,21,14,11)(10,17,18,24,19,16,23,20);(9,11,14,21,15,22,13,12)(10,16,18,20,19,17,23,24);(7,8)(9,10)(11,20)(12,17)(13,18)(14,23)(15,19)(16,21)(22,24)300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#67568, C5×#67441, #14277902, … |
| maximal normal subgroup of | C5×#67568, C5×#67441, #14277902, … |
| maximal quotient of | C5×C8×D24, C5×C8×#204, C5×C8×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4394);