Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×SD32 ⋊ C2 |
| Sylow | C19 ⋊ #510 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^c=g^18115 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#510, C2×#11926983, #14576767, … |
| maximal normal subgroup of | D19×#510, C2×#11926983, #14576767, … |
| maximal quotient of | #14565344, #14565353, #14565422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 988);