Finite Group DatabasebetaFinite Group Databasebeta| order | 22468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D137 |
| unambiguous semidirect product | (D41×C137)⋊C2 |
| unambiguous semidirect product | (C41×D137)⋊C2 |
| unambiguous semidirect product | D5617⋊C2 |
| Fitting, socle, derived, Hall | C41×C137 ⋊ C22 |
| Sylow | C137 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C137 | C22 |
| LCS | G ▷ C41×C137 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5617 |
1540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22468, 12);