Finite Group DatabasebetaFinite Group Databasebeta| order | 24126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D4021⋊C3 |
| unambiguous semidirect product | (C4021⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C4021 ⋊ C2×C3 |
| Hall | C4021⋊C3 ⋊ C2 |
| Hall | D4021 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C4021 | C2×C3 |
| LCS | G ▷ C4021 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4021 |
Polycyclic presentation:
2,3,4021|c^a=c^4020,c^b=c^2208676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24126, 1);