Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^18,c^b=ce,e^b=ef,g^b=g^18310 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#359, C2×#11926352, #14565361, … |
| maximal normal subgroup of | D19×#359, C2×#11926352, #14565361, … |
| maximal quotient of | #14561597, #14561600, #14561651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 357);