Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #417 |
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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,d^2=f,b^a=bd,d^a=df,g^a=g^18,c^b=cf,d^b=df202 conjugacy classes — view the full character table.
| maximal subgroup of | #14563589, #14563590, #14563594, … |
| maximal normal subgroup of | #14563589, #14563590, #14563594, … |
| maximal quotient of | #14562022, #14562048, #14562074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 550);