Finite Group DatabasebetaFinite Group Databasebeta| order | 28820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #28385659⋊C2 |
| unambiguous semidirect product | #28385665⋊C2 |
| unambiguous semidirect product | #28385671⋊C2 |
| Fitting, socle, derived, Hall | C11×C131 ⋊ C22×C5 |
| Hall | #20297885 ⋊ C22 |
| Hall | D11×D131 ⋊ C5 |
| Sylow | C131 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×D131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C131 | C22×C5 |
| LCS | G ▷ C11×C131 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1441 |
Polycyclic presentation:
2^2,5,11,131|e^a=e^130,d^b=d^10,d^c=d^4,e^c=e^89113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28820, 37);