Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #362 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cef,d^b=df,e^b=ef,g^b=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#362, C2×#11926359, #14565381, … |
| maximal normal subgroup of | D19×#362, C2×#11926359, #14565381, … |
| maximal quotient of | #14561604, #14561652, #14561683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 364);