Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C149 ⋊ #407 |
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,149|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^105,g^c=g^148,g^e=g^148620 conjugacy classes — view the full character table.
| maximal subgroup of | #34059538, #34059563, #34059572, … |
| maximal normal subgroup of | #34059538, #34059563, #34059572, … |
| maximal quotient of | #34059937, #34059940, #34059943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1520);