Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #443 |
| Sylow | C5 ⋊ #4824 |
| Sylow | C3 ⋊ #65184 |
212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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|b^2=e,c^2=e,d^2=f,e^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df90 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4824, #14417860, C2×#11748174, … |
| maximal normal subgroup of | D5×#4824, #14417860, C2×#11748174, … |
| maximal quotient of | #14286088, #14286155, #14286182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2369);