Finite Group DatabasebetaFinite Group Databasebeta| order | 33635 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C31 · Schur multiplier (H2) = C1 |
| direct product | C7×C31×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊(C5×C7×C31) |
| unambiguous semidirect product | (C7×C31)⋊(C5×C31) |
| Fitting, socle, Hall | C7×C312 ⋊ C5 |
| derived | C31 ⋊ C5×C7×C31 |
| Sylow | C312 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C31 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C312 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C7×C31 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1085 |
2387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33635, 4);