Finite Group DatabasebetaFinite Group Databasebeta| order | 33170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×D107 |
| unambiguous semidirect product | C107⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D107)⋊C5 |
| Fitting, socle, derived, Hall | C31×C107 ⋊ C2×C5 |
| Hall | C107×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C31×D107 ⋊ C5 |
| Sylow | C107 ⋊ C2×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C107 | C2×C5 |
| LCS | G ▷ C31×C107 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3317 |
605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33170, 10);