Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,e^2=f,b^a=bd,c^b=cf,g^b=g^18316 conjugacy classes — view the full character table.
| maximal subgroup of | #14561560, #14563585, #14563600, … |
| maximal normal subgroup of | #14561560, #14563585, #14563600, … |
| maximal quotient of | #14561981, #14561986, #14561990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 515);