Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #468 |
| Sylow | C5 ⋊ #5042 |
| Sylow | C3 ⋊ #65101 |
240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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|b^2=f,c^2=e,d^2=f,b^a=bef,c^a=ce,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df78 conjugacy classes — view the full character table.
| maximal subgroup of | #14427913, D5×#5042, C2×#11747345, … |
| maximal normal subgroup of | #14427913, D5×#5042, C2×#11747345, … |
| maximal quotient of | #14292395, #14292458, #14292677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1540);