Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #458 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=f,b^a=bd,c^a=ce,g^a=g^18,e^b=ef,d^c=df169 conjugacy classes — view the full character table.
| maximal subgroup of | #14565623, #14565624, #14565629, … |
| maximal normal subgroup of | #14565623, #14565624, #14565629, … |
| maximal quotient of | #14562621, #14562626, #14562632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 739);