Finite Group DatabasebetaFinite Group Databasebeta| order | 32124 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #24924182⋊C3 |
| Fitting, socle, derived, Sylow | C2677 ⋊ C3×C4 |
| Hall | #24924182 ⋊ C3 |
| Hall | C2677⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2677 | C3×C4 |
| prime radical | D2677⋊C3 | C2 |
| cosocle | D2677 | C2×C3 |
| LCS | G ▷ C2677 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2677 |
Polycyclic presentation:
2,3,2,2677|a^2=c,d^a=d^2127,d^b=d^1643,d^c=d^2676235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32124, 8);