Finite Group DatabasebetaFinite Group Databasebeta| order | 32469 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×C79⋊C3 |
| unambiguous semidirect product | C79⋊(C3×C137) |
| unambiguous semidirect product | (C79×C137)⋊C3 |
| Fitting, socle, Hall | C79×C137 ⋊ C3 |
| derived, Sylow | C79 ⋊ C3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | C79⋊C3 |
| commutator, cosocle, hypocenter | C79 | C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C79×C137 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C137 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10823 |
3973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32469, 1);