Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #397 |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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|a^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^18,c^b=cf202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#397, C2×#11926472, #14566877, … |
| maximal normal subgroup of | D19×#397, C2×#11926472, #14566877, … |
| maximal quotient of | #14561878, #14561882, #14561884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 477);