Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C27 · Schur multiplier (H2) = C36 |
| direct product | C32×(C37⋊C3)⋊C27 |
| unambiguous semidirect product | (C37⋊C3)⋊(C32×C27) |
| derived, Sylow | C37 ⋊ C33×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | #66526 |
| commutator, hypocenter | C37 | C33×C27 |
| Frattini | C3 | C33×#66526 |
| Fitting | C32×C9×C37 | C9 |
| socle | C33×C37 | C3×C9 |
| prime radical | C33×C37⋊C3 | C9 |
| cosocle | #66524 | C34 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32×C9 | |
1160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8991 |
1053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4416);