Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×M16 |
| Sylow | C5 ⋊ Dic3×M16 |
| Sylow | C3 ⋊ M16×AGL(1,𝔽5) |
284 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 106 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^2=e,d^2=f,e^2=f,c^a=cf,h^a=h^2,c^b=cf,g^b=g^2,h^d=h^478 conjugacy classes — view the full character table.
| maximal subgroup of | #14295452, #14295455, #14295495, … |
| maximal normal subgroup of | #14295452, #14295455, #14295495, … |
| maximal quotient of | #14280413, #14280415, #14280424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5893);