Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C19 ⋊ #533 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^18316 conjugacy classes — view the full character table.
| maximal subgroup of | #14562037, #14562039, #14562055, … |
| maximal normal subgroup of | #14562037, #14562039, #14562055, … |
| maximal quotient of | #14566042, #14566112, #14566118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1106);