Finite Group DatabasebetaFinite Group Databasebeta| order | 33170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C107⋊(D31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D107 |
| unambiguous semidirect product | D3317⋊C5 |
| Fitting, socle, derived, Hall | C31×C107 ⋊ C2×C5 |
| Hall | C107×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D3317 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D107 |
| Sylow | C107 ⋊ D31⋊C5 |
| 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 |
Polycyclic presentation:
2,5,31,107|c^a=c^30,d^a=d^106,c^b=c^16596 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33170, 12);