Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=df,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^18,e^c=ef145 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#464, C2×#11926764, #14573085, … |
| maximal normal subgroup of | D19×#464, C2×#11926764, #14573085, … |
| maximal quotient of | #14563049, #14563063, #14563077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 769);