Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #394 |
| Sylow | C5 ⋊ #4959 |
| Sylow | C3 ⋊ #65248 |
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,b^a=be,c^a=cd,g^a=g^2,h^a=h^4,c^b=cf162 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#394, C2×#11751060, D5×#4959, … |
| maximal normal subgroup of | D15×#394, C2×#11751060, D5×#4959, … |
| maximal quotient of | #14280028, #14280053, #14280056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5255);