Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #350 |
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=f,d^2=e,e^2=f,b^a=bc,g^a=g^18,c^b=cf,d^b=df208 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#350, C2×#11926328, #14565261, … |
| maximal normal subgroup of | D19×#350, C2×#11926328, #14565261, … |
| maximal quotient of | #14561561, #14561577, D4⋊(C19⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 333);