Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D1681 |
| unambiguous semidirect product | (D5×C1681)⋊C2 |
| unambiguous semidirect product | (C5×D1681)⋊C2 |
| unambiguous semidirect product | D8405⋊C2 |
| Fitting, derived, Hall | C5×C1681 ⋊ C22 |
| Sylow | C1681 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D1681 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C1681 | C22 |
| Frattini | C41 | D5×D41 |
| socle | C5×C41 | C2×D41 |
| LCS | G ▷ C5×C1681 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8405 |
3368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 17);