Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C4×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ #518 |
| Sylow | C5 ⋊ #5521 |
| Sylow | C3 ⋊ #66258 |
676 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=e,c^2=f,d^a=df,h^a=h^2,c^b=cf,g^b=g^2,h^e=h^472 conjugacy classes — view the full character table.
| maximal subgroup of | #14299609, #14299610, #14301472, … |
| maximal normal subgroup of | #14299609, #14299610, #14301472, … |
| maximal quotient of | #14319657, #14319706, #14319764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11032);