Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #387 |
| Sylow | C5 ⋊ #4654 |
| Sylow | C3 ⋊ #64944 |
308 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=e,b^2=ef,c^2=d,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 | #14320372, C2×#11748810, D5×#4654, … |
| maximal normal subgroup of | #14320372, C2×#11748810, D5×#4654, … |
| maximal quotient of | #14279912, #14279971, #14279974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3005);