Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D19 |
| commutator, socle | C2×C19 | C22×C16 |
| Fitting | C19×#504 | C2 |
| prime radical | #41×C19 | C8 |
| cosocle | C16×C19 | C23 |
| hypercenter | #504 | D19 |
| hypocenter | C19 | #2258 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^7,19|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^18,c^b=cg440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 6804);