Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 488 |
Polycyclic presentation:
2^5,61|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^11,c^b=ce,f^d=f^6089 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14519841, D61⋊#104, #16840759, … |
| maximal normal subgroup of | C2×#14519841, D61⋊#104, #16840759, … |
| maximal quotient of | D4⋊#92420, #16840612, #16840613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 210);