Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C3×C4×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ #551 |
| Sylow | C5 ⋊ #5556 |
| Sylow | C3 ⋊ #65890 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^a=def,h^a=h^4,c^b=cf,d^b=df,g^b=g^2117 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5556, D3×#65890, C2×#11754677, … |
| maximal normal subgroup of | D5×#5556, D3×#65890, C2×#11754677, … |
| maximal quotient of | #14326343, #14326345, #14326514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8872);