Finite Group DatabasebetaFinite Group Databasebeta| order | 29727 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C367⋊C3 |
| Fitting | C27×C367 ⋊ C3 |
| derived, Sylow | C367 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C367⋊C3 |
| commutator, hypocenter | C367 | C3×C27 |
| Frattini | C9 | C3×C367⋊C3 |
| Fitting | C27×C367 | C3 |
| socle | C3×C367 | C3×C9 |
| prime radical | C3×C367⋊C3 | C9 |
| cosocle | C9×C367 | C32 |
| LCS | G ▷ C367 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9909 |
3375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29727, 23);