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×SD16 |
| Sylow | C5 ⋊ #4852 |
| Sylow | C3 ⋊ C4×#677 |
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 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) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=d,c^2=e,e^2=f,c^a=ce,e^a=ef,h^a=h^4,g^b=g^2138 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#1200, C4×D3×#677, C2×#11747789, … |
| maximal normal subgroup of | SD16×#1200, C4×D3×#677, C2×#11747789, … |
| maximal quotient of | #14286190, #14286652, #14286747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1984);