Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C19×Q32 ⋊ C2 |
| Sylow | C19 ⋊ SD64 |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^18118 conjugacy classes — view the full character table.
| maximal subgroup of | D19×SD64, C2×#11926381, #14565942, … |
| maximal normal subgroup of | D19×SD64, C2×#11926381, #14565942, … |
| maximal quotient of | #14561812, #14561816, #14561836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 386);