Finite Group DatabasebetaFinite Group Databasebeta| order | 22940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C37 · Schur multiplier (H2) = C2 |
| direct product | C22×C37×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C22×C31)⋊(C5×C37) |
| unambiguous semidirect product | (C22×C31×C37)⋊C5 |
| Fitting, socle, Hall | C22×C31×C37 ⋊ C5 |
| derived, Sylow | C31 ⋊ C22×C5×C37 |
| Hall | C31×C37 ⋊ C22×C5 |
| Hall | C22×C31 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C37 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C22×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C22×C31×C37 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C37 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4588 |
1628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22940, 20);