Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×C16 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×M32 |
| Sylow | C5 ⋊ D3×M32 |
| Sylow | C3 ⋊ D5×M32 |
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=d,d^2=e,e^2=f,c^a=cf,h^a=h^4,c^b=cf,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #14312730, #14312732, #14312775, … |
| maximal normal subgroup of | #14312730, #14312732, #14312775, … |
| maximal quotient of | #14312557, #14312600, #14312602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1004);