Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of D177 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic177 |
| unambiguous semidirect product | C3⋊(C3×Dic59) |
| unambiguous semidirect product | C59⋊(C3×Dic3) |
| derived | C3×C59 ⋊ C3×C4 |
| Hall | C32×C59 ⋊ C4 |
| Sylow | C59 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D177 |
| commutator, hypocenter | C3×C59 | C3×C4 |
| Frattini | C2 | C3×D177 |
| Fitting, socle, prime radical | C2×C32×C59 | C2 |
| cosocle | C2×C3×C59 | C2×C3 |
| LCS | G ▷ C3×C59 | |
| UCS | C1 ◁ C2×C3 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 708 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 14);