Finite Group DatabasebetaFinite Group Databasebeta| order | 17980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C29⋊(D31⋊C5) |
| unambiguous semidirect product | (C2×C29)⋊(D31⋊C5) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽32))⋊D29 |
| unambiguous semidirect product | (C2×D899)⋊C5 |
| Fitting, socle | C2×C29×C31 ⋊ C2×C5 |
| derived, Hall | C29×C31 ⋊ C22×C5 |
| Hall | C29×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×D899 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×D29 |
| Sylow | C31 ⋊ C2×C5×D29 |
| Sylow | C29 ⋊ C2×D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C29⋊(D31⋊C5) |
| commutator, cosocle, hypocenter | C29×C31 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C31 | C2×C5 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1798 |
334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17980, 18);