Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C149 ⋊ C2 |
| Sylow | C149 ⋊ #551 |
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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,b^2=f,b^a=be,c^a=cf,d^b=de,g^b=g^148,g^d=g^1481061 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #551×D149, C2×#23750302, #34058243, … |
| maximal normal subgroup of | #551×D149, C2×#23750302, #34058243, … |
| maximal quotient of | #34047537, #34047538, #34047549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1226);