Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #342 |
| Sylow | C5 ⋊ #4526 |
| Sylow | C3 ⋊ #64746 |
284 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 95 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|a^2=c,b^2=d,b^a=be,e^a=ef,g^a=g^2,h^a=h^4,c^b=cf162 conjugacy classes — view the full character table.
| maximal subgroup of | #14278076, #14278079, #14278087, … |
| maximal normal subgroup of | #14278076, #14278079, #14278087, … |
| maximal quotient of | #14276819, #14276851, #14276905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 542);