Finite Group DatabasebetaFinite Group Databasebeta| order | 36108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(C59⋊#595) |
| unambiguous semidirect product | C3⋊(C3×C59⋊#595) |
| unambiguous semidirect product | C59⋊(C3×C3⋊#595) |
| Fitting, socle, Hall | C32×C17×C59 ⋊ C4 |
| derived | C3×C17×C59 ⋊ C3×C4 |
| Hall | C17×C59 ⋊ C3×Dic3 |
| Hall | C32×C59 ⋊ #595 |
| Hall | C32×C17 ⋊ Dic59 |
| Sylow | C59 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3×Dic177 |
| Sylow | C32 ⋊ C59⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C59⋊#595) |
| commutator, hypocenter | C3×C17×C59 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C59 | C4 |
| prime radical | C32×D17×C59 | C2 |
| cosocle | C3×D17×C59 | C2×C3 |
| LCS | G ▷ C3×C17×C59 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6018 |
2664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36108, 53);