Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C149 ⋊ C4 |
| Sylow | C149 ⋊ #421 |
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^105,c^b=cf,d^b=df,g^c=g^148,g^e=g^148392 conjugacy classes — view the full character table.
| maximal subgroup of | #34060541, #34060544, #34060689, … |
| maximal normal subgroup of | #34060541, #34060544, #34060689, … |
| maximal quotient of | #34059987, #34059990, #34059995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1547);