Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #1843 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D19 |
| commutator, socle, prime radical | C23×C19 | C22×C4 |
| Fitting | C19×#376 | C2 |
| cosocle | C22×C4×C19 | C23 |
| hypercenter | #376 | D19 |
| hypocenter | C19 | #1843 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2432 |
Polycyclic presentation:
2^7,19|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^18,c^b=cg404 conjugacy classes — view the full character table.
| maximal subgroup of | #18076658, #18076659, #18086608, … |
| maximal normal subgroup of | #18076658, #18076659, #18086608, … |
| maximal quotient of | #18076292, #18076295, #18076299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 4664);