Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×C22⋊C8 ⋊ C2 |
| Sylow | C19 ⋊ #408 |
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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,e^2=f,b^a=bd,c^b=cf,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#408, C2×#11926509, #14572077, … |
| maximal normal subgroup of | D19×#408, C2×#11926509, #14572077, … |
| maximal quotient of | #14561980, #14561982, #14561985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 514);