Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #508 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^18,d^b=de,e^b=ef,g^b=g^18310 conjugacy classes — view the full character table.
| maximal subgroup of | #14561818, #14561820, #14561821, … |
| maximal normal subgroup of | #14561818, #14561820, #14561821, … |
| maximal quotient of | #14565343, #14565419, C4×D304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 981);