Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #551 |
| Sylow | C5 ⋊ #5705 |
| Sylow | C3 ⋊ #65861 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^2=f,c^a=cf,d^a=de,h^a=h^4,c^b=cf,g^b=g^2,d^c=df99 conjugacy classes — view the full character table.
| maximal subgroup of | #14483260, D3×#65861, C2×#11753919, … |
| maximal normal subgroup of | #14483260, D3×#65861, C2×#11753919, … |
| maximal quotient of | #14326256, #14326332, #14326467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8114);