Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C5×#127 ⋊ C2 |
| Hall | C3×C5 ⋊ #496 |
| Sylow | C5 ⋊ #5074 |
| Sylow | C3 ⋊ #65363 |
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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=ef,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^4,c^b=cef,d^c=df114 conjugacy classes — view the full character table.
| maximal subgroup of | #14290881, #14290888, #14290900, … |
| maximal normal subgroup of | #14290881, #14290888, #14290900, … |
| maximal quotient of | #14293653, #14293716, #14293794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5370);