Finite Group DatabasebetaFinite Group Databasebeta| order | 23124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D123⋊D47 |
| unambiguous semidirect product | D141⋊D41 |
| unambiguous semidirect product | D1927⋊D3 |
| Fitting, socle, derived, Hall | C3×C41×C47 ⋊ C22 |
| Hall | C41×C47 ⋊ C2×D3 |
| Hall | C3×C47 ⋊ C2×D41 |
| Hall | C3×C41 ⋊ C2×D47 |
| Sylow | C47 ⋊ D3×D41 |
| Sylow | C41 ⋊ D3×D47 |
| Sylow | C3 ⋊ D41×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C41×C47 | C22 |
| LCS | G ▷ C3×C41×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5781 |
Polycyclic presentation:
2^2,3,41,47|d^a=d^40,e^a=e^46,c^b=c^2,d^b=d^401515 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23124, 20);