Finite Group DatabasebetaFinite Group Databasebeta| order | 22940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic37 |
| unambiguous semidirect product | Dic1147⋊C5 |
| derived, Hall | C31×C37 ⋊ C4×C5 |
| Hall | C37×ΓL(1,𝔽32) ⋊ C4 |
| Hall | Dic1147 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ Dic37 |
| Sylow | C37 ⋊ Dic31⋊C5 |
| Sylow | C31 ⋊ C5×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C37⋊(D31⋊C5) |
| commutator, hypocenter | C31×C37 | C4×C5 |
| Fitting, socle, cosocle | C2×C31×C37 | C2×C5 |
| prime radical | C2×C37×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4588 |
Polycyclic presentation:
2,5,31,37,2|a^2=e,c^a=c^30,d^a=d^36,c^b=c^16422 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22940, 12);