Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×#342 ⋊ C2 |
| Sylow | C19 ⋊ #2032 |
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^7,19|a^2=d,b^2=d,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^18,d^c=dg,h^c=h^18221 conjugacy classes — view the full character table.
| maximal quotient of | #18085686, #18085688, #18085690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 5688);