Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #436 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^18,c^b=cf,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | #14562465, #14562467, #14562479, … |
| maximal normal subgroup of | #14562465, #14562467, #14562479, … |
| maximal quotient of | #14562520, #14562526, #14562532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 627);