Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#107 ⋊ C2 |
| Sylow | C19 ⋊ #480 |
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^18,g^b=g^18,e^c=ef145 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#480, C2×#11926859, #14573552, … |
| maximal normal subgroup of | D19×#480, C2×#11926859, #14573552, … |
| maximal quotient of | #14563720, #14563821, #14563951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 864);