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 ⋊ #417 |
| Sylow | C5 ⋊ #5133 |
| Sylow | C3 ⋊ #65092 |
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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|b^2=e,c^2=de,d^2=f,c^a=cf,h^a=h^4,c^b=cd,d^b=df,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #14412488, D5×#5133, C2×#11747606, … |
| maximal normal subgroup of | #14412488, D5×#5133, C2×#11747606, … |
| maximal quotient of | #14281660, #14281958, #14282256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1801);