Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C61 ⋊ C2 |
| Sylow | C61 ⋊ SD32 |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^5,61|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^60221 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D61, C2×#14519720, #16840192, … |
| maximal normal subgroup of | SD32×D61, C2×#14519720, #16840192, … |
| maximal quotient of | #16839562, #16839566, #16839589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 89);