Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C19×#125 ⋊ C2 |
| Sylow | C19 ⋊ #490 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^18,c^b=cf,g^b=g^18,g^c=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | #14562928, #14562930, #14562933, … |
| maximal normal subgroup of | #14562928, #14562930, #14562933, … |
| maximal quotient of | #14563768, #14564331, #14564458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 915);