Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #362 |
| Sylow | C5 ⋊ #4496 |
| Sylow | C3 ⋊ #64716 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^2,h^a=h^4,d^b=def,e^b=ef114 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#362, C2×#11746317, D5×#4496, … |
| maximal normal subgroup of | D15×#362, C2×#11746317, D5×#4496, … |
| maximal quotient of | #14277866, #14278234, #14278468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 512);