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 80 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 80 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=d,b^2=df,c^2=f,e^2=f,h^a=h^4,c^b=ce,e^b=ef,g^b=g^2,e^c=ef96 conjugacy classes — view the full character table.
| maximal subgroup of | #14286262, #14286264, #14286416, … |
| maximal normal subgroup of | #14286262, #14286264, #14286416, … |
| maximal quotient of | #14286244, #14286809, #14286832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3439);