Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ #536 |
| Sylow | C5 ⋊ #5816 |
| Sylow | C3 ⋊ #65860 |
540 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 160 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|a^2=f,b^2=e,d^2=f,b^a=be,d^a=df,h^a=h^4,c^b=cf,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #14302796, #14302802, #14302950, … |
| maximal normal subgroup of | #14302796, #14302802, #14302950, … |
| maximal quotient of | #14322492, #14322546, #14322928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8473);