Finite Group DatabasebetaFinite Group Databasebeta| order | 27306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D333 |
| unambiguous semidirect product | C9⋊(C41×D37) |
| unambiguous semidirect product | C37⋊(D9×C41) |
| Fitting, Hall | C9×C37×C41 ⋊ C2 |
| derived, Hall | C9×C37 ⋊ C2×C41 |
| Hall | C37×C41 ⋊ D9 |
| Hall | C9×C41 ⋊ D37 |
| Sylow | C37 ⋊ D9×C41 |
| Sylow | C9 ⋊ C41×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D333 |
| commutator, cosocle, hypocenter | C9×C37 | C2×C41 |
| Frattini | C3 | C41×D111 |
| Fitting | C9×C37×C41 | C2 |
| socle | C3×C37×C41 | D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 ◁ C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13653 |
6888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27306, 8);