Finite Group DatabasebetaFinite Group Databasebeta| order | 32706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D79⋊C9) |
| unambiguous semidirect product | (C79⋊C9)⋊D23 |
| unambiguous semidirect product | D1817⋊C9 |
| derived, Hall | C23×C79 ⋊ C2×C9 |
| Hall | C23×C79⋊C9 ⋊ C2 |
| Hall | D1817 ⋊ C9 |
| Hall | C79⋊C9 ⋊ D23 |
| Sylow | C79 ⋊ C9×D23 |
| Sylow | C23 ⋊ D79⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C23⋊(D79⋊C3) |
| commutator, hypocenter | C23×C79 | C2×C9 |
| Fitting, socle, cosocle | C3×C23×C79 | C2×C3 |
| prime radical | C3×D1817 | C3 |
| LCS | G ▷ C23×C79 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16353 |
Polycyclic presentation:
2,3,23,79,3|b^3=e,c^a=c^22,d^a=d^78,d^b=d^231014 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32706, 12);