Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #544 |
| Sylow | C5 ⋊ #5729 |
| Sylow | C3 ⋊ #66023 |
412 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 136 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=f,c^2=e,d^2=ef,b^a=be,d^a=df,h^a=h^4,d^b=def,g^b=g^2,d^c=de84 conjugacy classes — view the full character table.
| maximal subgroup of | #14430820, #14430835, #14430898, … |
| maximal normal subgroup of | #14430820, #14430835, #14430898, … |
| maximal quotient of | #14322858, #14322945, #14322950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 7584);