Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #489 |
| Sylow | C5 ⋊ #4765 |
| Sylow | C3 ⋊ #65054 |
200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 58 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,d^2=f,b^a=be,c^a=cd,d^a=df,h^a=h^4,c^b=cdef,d^b=df,g^b=g^2,d^c=df78 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4765, D3×#65054, C2×#11749117, … |
| maximal normal subgroup of | D5×#4765, D3×#65054, C2×#11749117, … |
| maximal quotient of | #14298869, #14304666, #14304668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3312);