Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×#135 ⋊ C2 |
| Hall | C3×C5 ⋊ #508 |
| Sylow | C5 ⋊ #5194 |
| Sylow | C3 ⋊ #65483 |
168 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^2,h^a=h^4,d^c=de,e^c=ef120 conjugacy classes — view the full character table.
| maximal subgroup of | #14315622, #14315625, #14315647, … |
| maximal normal subgroup of | #14315622, #14315625, #14315647, … |
| maximal quotient of | #14313845, #14313851, #14314589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5490);