Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#11924753 |
| Sylow | C149 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,149|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^105,c^b=ce,g^d=g^148398 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#11924753, D149⋊(D4⋊C8), #34059982, … |
| maximal normal subgroup of | C2×D4⋊#11924753, D149⋊(D4⋊C8), #34059982, … |
| maximal quotient of | #34059507, #34059509, #34059527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1396);