Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #468 |
| Sylow | C5 ⋊ #4812 |
| Sylow | C3 ⋊ #65069 |
240 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 60 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,c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,h^a=h^4,c^b=cdf,d^b=df,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | #14427919, C2×#11747929, D3×#65069, … |
| maximal normal subgroup of | #14427919, C2×#11747929, D3×#65069, … |
| maximal quotient of | #14292397, #14292460, #14292679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2124);