Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C24×C3×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #379 |
| Sylow | C5 ⋊ #5247 |
| Sylow | C3 ⋊ #65800 |
1012 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^a=bf,c^a=ce,g^a=g^2,h^a=h^3,h^d=h^4108 conjugacy classes — view the full character table.
| maximal subgroup of | #14277356, #14277358, #14296835, … |
| maximal normal subgroup of | #14277356, #14277358, #14296835, … |
| maximal quotient of | #14279868, #14280036, #14280297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6654);