Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×C4⋊Q8 ⋊ C2 |
| Sylow | C19 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^18145 conjugacy classes — view the full character table.
| maximal subgroup of | #14562811, #14562813, #14562832, … |
| maximal normal subgroup of | #14562811, #14562813, #14562832, … |
| maximal quotient of | #14563007, #14563021, #14563031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 751);