Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #104×C149 ⋊ C2 |
| Sylow | C149 ⋊ #456 |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^148,d^b=df,e^b=ef,d^c=df,g^c=g^1481052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #456×D149, C2×#23749809, #34054036, … |
| maximal normal subgroup of | #456×D149, C2×#23749809, #34054036, … |
| maximal quotient of | #34043655, #34043657, #34043661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 733);