Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D32⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ #685 |
| Sylow | C5 ⋊ D32⋊C4 |
116 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3^2,5|b^2=d,b^a=bc,e^a=e^2,f^a=e^2f,g^a=g^4,e^b=e^2f^2,e^c=e^2,f^c=f^254 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D32⋊C4, #13088445, #13088447, … |
| maximal normal subgroup of | D5×D32⋊C4, #13088445, #13088447, … |
| maximal quotient of | #13085572, #13085574, #13085576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 472);