Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #343 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#343, C2×#11926312, #14563372, … |
| maximal normal subgroup of | D19×#343, C2×#11926312, #14563372, … |
| maximal quotient of | #14561477, #14561484, #14561486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 317);