Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #451 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^18145 conjugacy classes — view the full character table.
| maximal subgroup of | #14562592, #14562593, #14562598, … |
| maximal normal subgroup of | #14562592, #14562593, #14562598, … |
| maximal quotient of | #14562591, #14562608, #14562659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 704);