Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C19 ⋊ #3555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C19×#529 | C2 |
| prime radical | C19×#121 | C22 |
| hypercenter | #529 | D19 |
| hypocenter | C19 | #3555 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #529 | |
910 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^7,19|a^2=f,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^18,c^b=cg,d^b=df,h^b=h^18290 conjugacy classes — view the full character table.
| maximal subgroup of | #18074949, #18074953 |
| maximal normal subgroup of | #18074949, #18074953 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 19000);