Finite Group DatabasebetaFinite Group Databasebeta| order | 29450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D19×ΓL(1,𝔽32) |
| unambiguous semidirect product | C19⋊(C2×C5×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D19)⋊C52 |
| unambiguous semidirect product | (C5×C31×D19)⋊C5 |
| Fitting, socle | C5×C19×C31 ⋊ C2×C5 |
| derived, Hall | C19×C31 ⋊ C2×C52 |
| Hall | C5×C19×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C31×D19 ⋊ C52 |
| Sylow | C31 ⋊ C52×D19 |
| Sylow | C19 ⋊ C2×C5×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D19×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C19×C31 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C31 | C2×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29450, 16);