Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C19 ⋊ #2840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C19×#379 | C2 |
| prime radical | C25×C19 | C22 |
| hypercenter | #379 | D19 |
| hypocenter | C19 | #2840 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #379 | |
580 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^7,19|b^2=g,c^2=g,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^18278 conjugacy classes — view the full character table.
| maximal subgroup of | #18085789, #18085790, #18085792, … |
| maximal normal subgroup of | #18085789, #18085790, #18085792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 12763);