Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C8×D4 |
| Sylow | C5 ⋊ C8×#67 |
| Sylow | C3 ⋊ #65014 |
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|c^2=d,d^2=f,b^a=be,h^a=h^4,c^b=ce,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #14315017, #14315019, #14315101, … |
| maximal normal subgroup of | #14315017, #14315019, #14315101, … |
| maximal quotient of | #14286084, #14286151, #14286186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1889);