Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #472 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,e^c=ef,g^c=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | #14565589, #14565591, #14565596, … |
| maximal normal subgroup of | #14565589, #14565591, #14565596, … |
| maximal quotient of | #14562987, #14562992, #14563031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 816);