Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×D8 |
| Sylow | C5 ⋊ C4×#213 |
| Sylow | C3 ⋊ #65161 |
268 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 78 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=e,b^2=e,c^2=e,d^2=f,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df96 conjugacy classes — view the full character table.
| maximal subgroup of | #14286112, #14286114, #14286479, … |
| maximal normal subgroup of | #14286112, #14286114, #14286479, … |
| maximal quotient of | #14286089, #14286523, #14286548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1418);