Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11924746 |
| Sylow | C149 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,149|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^148,c^b=ce1508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D149, C2×Q8⋊#11924746, #34043072, … |
| maximal normal subgroup of | Q8⋊C8×D149, C2×Q8⋊#11924746, #34043072, … |
| maximal quotient of | #34042514, #34042517, #34042532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 280);