Finite Group DatabasebetaFinite Group Databasebeta| order | 32798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23×C31 · Schur multiplier (H2) = C1 |
| direct product | C23×C31×D23 |
| unambiguous semidirect product | C23⋊(C2×C23×C31) |
| Fitting, socle, Hall | C232×C31 ⋊ C2 |
| derived | C23 ⋊ C2×C23×C31 |
| Sylow | C232 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C31 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C23×C31 |
| Frattini | C1 | G |
| Fitting, socle | C232×C31 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C23×C31 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1426 |
9269 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32798, 7);