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 ⋊ #328 |
| Sylow | C5 ⋊ #4452 |
| Sylow | C3 ⋊ #64687 |
160 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 52 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=c,b^2=cd,d^2=ef,b^a=bd,d^a=de,h^a=h^4,c^b=cf,d^b=df,g^b=g^2111 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4452, #14282725, C2×#11745964, … |
| maximal normal subgroup of | D5×#4452, #14282725, C2×#11745964, … |
| maximal quotient of | #14276668, #14276685, #14277146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 159);