Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#41 ⋊ Dic3 |
| Sylow | C5 ⋊ #5424 |
158 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^3,3,5,2^3|a^2=c,b^2=h,f^2=h,g^2=h,d^a=d^2,e^a=e^3,f^a=gh,g^a=fh,e^c=e^4,f^d=g,g^d=fgh,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #14512413, #14512414, #14512419, … |
| maximal normal subgroup of | #14512413, #14512414, #14512419, … |
| maximal quotient of | #14512441, #14512442, C4×#91886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10920);