Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #423 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^b=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | #14561585, #14563625, #14563626, … |
| maximal normal subgroup of | #14561585, #14563625, #14563626, … |
| maximal quotient of | #14562390, #14562393, #14562396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 572);