Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C19×#585 ⋊ C2 |
| Sylow | C19 ⋊ #3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D19 |
| commutator, cosocle | C4×C19 | C25 |
| Frattini | C4 | C24×D19 |
| Fitting | C19×#585 | C2 |
| socle | C2×C19 | C23×D4 |
| hypercenter | #585 | D19 |
| hypocenter | C19 | #3585 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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|f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,h^b=h^18,d^c=dg347 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 19289);