Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#487 ⋊ C2 |
| Sylow | C19 ⋊ #1638 |
194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^7,19|a^2=f,b^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^18224 conjugacy classes — view the full character table.
| maximal quotient of | #18071413, #18071427, #18071469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 3679);