Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #346 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | #14561770, D19×#346, C2×#11926319, … |
| maximal normal subgroup of | #14561770, D19×#346, C2×#11926319, … |
| maximal quotient of | #14561551, #14561554, #14561712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 324);