Finite Group DatabasebetaFinite Group Databasebeta| order | 23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C31⋊C3)⋊D43) |
| unambiguous semidirect product | (C31⋊C3)⋊D129 |
| Fitting, socle, derived | C3×C31×C43 ⋊ C2×C3 |
| Hall | C3×C43×C31⋊C3 ⋊ C2 |
| Hall | C31×C43 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ D43 |
| Sylow | C43 ⋊ C3⋊(D31⋊C3) |
| Sylow | C31 ⋊ C3×D129 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C43 | C2×C3 |
| LCS | G ▷ C3×C31×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3999 |
Polycyclic presentation:
2,3^2,31,43|c^a=c^2,d^a=d^30,e^a=e^42,d^b=d^5843 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23994, 49);