Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ Q8×D5 |
| Sylow | C5 ⋊ #3797 |
168 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 52 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:
2^4,3^2,5|a^2=d,b^2=d,c^2=d,c^a=cd,f^a=f^2,g^a=g^4,c^b=cd,e^b=e^278 conjugacy classes — view the full character table.
| maximal subgroup of | #13085693, #13085703, #13085711, … |
| maximal normal subgroup of | #13085693, #13085703, #13085711, … |
| maximal quotient of | #13087295, #13087300, #13087303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 667);