Finite Group DatabasebetaFinite Group Databasebeta| order | 23124 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C47⋊#4223 |
| unambiguous semidirect product | C47⋊(C3×#4223) |
| Fitting, socle, Hall | C3×C41×C47 ⋊ C4 |
| derived, Hall | C41×C47 ⋊ C3×C4 |
| Hall | C3×C47 ⋊ #4223 |
| Hall | C3×C41 ⋊ Dic47 |
| Sylow | C47 ⋊ C3×#4223 |
| Sylow | C41 ⋊ C3×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C47⋊#4223 |
| commutator, hypocenter | C41×C47 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C47 | C4 |
| prime radical | C3×C47×D41 | C2 |
| cosocle | C47×D41 | C2×C3 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5781 |
1560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23124, 11);