Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#64515, #14561914, #14561917, … |
| maximal normal subgroup of | C8×#64515, #14561914, #14561917, … |
| maximal quotient of | #14563380, C4×(C2×D19)⋊C8, C4×Dic19⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 600);