Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #360 |
| Sylow | C5 ⋊ #4566 |
| Sylow | C3 ⋊ #64708 |
116 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|b^2=c,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,h^a=h^4,d^b=def,e^b=ef,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64708, D5×#4566, C2×#11745909, … |
| maximal normal subgroup of | D3×#64708, D5×#4566, C2×#11745909, … |
| maximal quotient of | #14277854, #14277877, #14278176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 104);