Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #475 |
| Sylow | C5 ⋊ #4791 |
| Sylow | C3 ⋊ #65143 |
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 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) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=d,c^2=ef,e^2=f,c^a=cde,e^a=ef,h^a=h^4,c^b=cef,e^b=ef,g^b=g^293 conjugacy classes — view the full character table.
| maximal subgroup of | #14430025, D5×#4791, C2×#11747880, … |
| maximal normal subgroup of | #14430025, D5×#4791, C2×#11747880, … |
| maximal quotient of | #14297706, #14300182, #14300188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2075);