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 ⋊ #5623 |
| Sylow | C3 ⋊ #65957 |
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=e,b^2=ef,d^2=e,c^a=cf,d^a=de,h^a=h^4,c^b=cf,d^b=def,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #14287871, #14287886, #14287889, … |
| maximal normal subgroup of | #14287871, #14287886, #14287889, … |
| maximal quotient of | #14322870, #14322902, #14324516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8378);