Finite Group DatabasebetaFinite Group Databasebeta| order | 32604 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊((C19⋊C3)⋊#261) |
| unambiguous semidirect product | (C19⋊C3)⋊(C11⋊#261) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C13×C19 | C3×C4 |
| prime radical | C11×D13×C19⋊C3 | C2 |
| cosocle | C11×C19×D13 | C2×C3 |
| LCS | G ▷ C11×C13×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2717 |
Polycyclic presentation:
2,3,2,11,13,19|a^2=c,d^a=d^10,e^a=e^5,f^a=f^18,f^b=f^7,e^c=e^12405 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32604, 84);