Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #1917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D19 |
| commutator, socle, prime radical | C23×C19 | C22×C4 |
| Fitting | C19×#336 | C2 |
| cosocle | C22×C4×C19 | C23 |
| hypercenter | #336 | D19 |
| hypocenter | C19 | #1917 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^7,19|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^18,c^b=cg,h^b=h^18,h^c=h^18404 conjugacy classes — view the full character table.
| maximal quotient of | #18080687, #18080694, #18080701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 5077);