Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×C22⋊C4 |
| Sylow | C5 ⋊ #4666 |
| Sylow | C3 ⋊ C4×C22⋊Dic5 |
516 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 164 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,c^2=e,b^a=bf,c^a=cf,h^a=h^4,g^b=g^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #14282840, #14282849, #14282850, … |
| maximal normal subgroup of | #14282840, #14282849, #14282850, … |
| maximal quotient of | Dic3×#3963, #14279874, #14279913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2914);