Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Hall | C3×C5 ⋊ #379 |
| Sylow | C5 ⋊ #4955 |
| Sylow | C3 ⋊ #65244 |
1012 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=de,b^a=be,c^a=cf,h^a=h^4,c^b=cf,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #14277560, #14296841, #14296844, … |
| maximal normal subgroup of | #14277560, #14296841, #14296844, … |
| maximal quotient of | #14279873, #14279876, #14280041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3697);