Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C19 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | #14561463, #14561464, #14561465, … |
| maximal normal subgroup of | #14561463, #14561464, #14561465, … |
| maximal quotient of | #14563381, C4×C22⋊(C19⋊C8), C4×C4⋊(C19⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 602);