Finite Group DatabasebetaFinite Group Databasebeta| order | 33170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C107 · Schur multiplier (H2) = C1 |
| direct product | C2×C107×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C31)⋊(C5×C107) |
| unambiguous semidirect product | (C2×C31×C107)⋊C5 |
| Fitting, socle, Hall | C2×C31×C107 ⋊ C5 |
| derived, Sylow | C31 ⋊ C2×C5×C107 |
| Hall | C31×C107 ⋊ C2×C5 |
| Hall | C2×C31 ⋊ C5×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C107 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C2×C5×C107 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C107 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C107 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6634 |
2354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33170, 2);