Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ C4×#216 |
| Sylow | C3 ⋊ #65079 |
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=e,b^2=f,c^2=ef,d^2=f,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df96 conjugacy classes — view the full character table.
| maximal subgroup of | #14286267, #14286269, #14286421, … |
| maximal normal subgroup of | #14286267, #14286269, #14286421, … |
| maximal quotient of | #14286238, #14286803, #14286838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1458);