Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C19×#336 ⋊ C2 |
| Sylow | C19 ⋊ #2015 |
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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=g,b^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^18,c^b=cf,d^b=dg,e^b=eg,h^b=h^18,d^c=dg,e^c=eg,h^c=h^18392 conjugacy classes — view the full character table.
| maximal quotient of | #18083025, #18083032, #18083046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 5607);