Finite Group DatabasebetaFinite Group Databasebeta| order | 33170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C107) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C107) |
| unambiguous semidirect product | (D31×C107)⋊C5 |
| Fitting, socle, Hall | C31×C107 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C107 |
| Hall | C107×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D31×C107 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C107 |
| Hall | D31 ⋊ C5×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C107 |
| Frattini | C1 | G |
| Fitting, socle | C31×C107 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C107 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3317 |
1391 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33170, 11);