Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66264⋊C3 |
| Hall | #66264 ⋊ C3 |
| Sylow | C5 ⋊ #568⋊C3 |
146 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^2,3,2^3,5,2|a^2=d,b^2=h,d^2=h,e^2=h,f^2=h,b^a=bh,g^a=g^2,e^c=ef,f^c=e,g^d=g^4,f^e=fh52 conjugacy classes — view the full character table.
| maximal subgroup of | #14512417, #14512418, #14512419, … |
| maximal normal subgroup of | #14512417, #14512418, #14512419, … |
| maximal quotient of | SL(2,𝔽3)×#700, #10617184⋊C3, #10617199⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10934);