Finite Group DatabasebetaFinite Group Databasebeta| order | 32844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D23×D51 |
| unambiguous semidirect product | (C3×D23)⋊(C7×D17) |
| unambiguous semidirect product | (C17×D23)⋊(D3×C7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D23×D51 |
| commutator, cosocle, hypocenter | C3×C17×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C23 | C22 |
| LCS | G ▷ C3×C17×C23 | |
| UCS | C1 ◁ C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8211 |
2457 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32844, 58);