Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #433 |
| Sylow | C5 ⋊ #4840 |
| Sylow | C3 ⋊ #64998 |
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 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) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=e,b^2=e,c^2=d,d^2=f,b^a=bf,c^a=ce,h^a=h^4,c^b=cf,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #14413842, D3×#64998, C2×#11747663, … |
| maximal normal subgroup of | #14413842, D3×#64998, C2×#11747663, … |
| maximal quotient of | #14294952, #14295118, #14296211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1858);