Finite Group DatabasebetaFinite Group Databasebeta| order | 17980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic29×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C31×Dic29)⋊C5 |
| derived, Hall | C29×C31 ⋊ C4×C5 |
| Hall | C29×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C31×Dic29 ⋊ C5 |
| Sylow | C31 ⋊ C5×Dic29 |
| Sylow | C29 ⋊ C4×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D29×ΓL(1,𝔽32) |
| commutator, hypocenter | C29×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C29×C31 | C2×C5 |
| prime radical | C2×C29×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3596 |
352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17980, 11);