Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #405 |
| Sylow | C5 ⋊ #4689 |
| Sylow | C3 ⋊ #65390 |
260 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 116 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=d,c^2=e,e^2=f,b^a=bf,h^a=h^4,g^b=g^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #14312655, #14312670, #14312671, … |
| maximal normal subgroup of | #14312655, #14312670, #14312671, … |
| maximal quotient of | C8×#6650, #14280454, #14280531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1848);