Finite Group DatabasebetaFinite Group Databasebeta| order | 32124 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#24924182 |
| Fitting, socle, Hall | C3×C2677 ⋊ C4 |
| derived, Sylow | C2677 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24924182 |
| commutator, hypocenter | C2677 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2677 | C4 |
| prime radical | C3×D2677 | C2 |
| cosocle | D2677 | C2×C3 |
| LCS | G ▷ C2677 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8031 |
2019 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32124, 10);