Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C9 · Schur multiplier (H2) = C310 |
| direct product | C34×#66526 |
| unambiguous semidirect product | (C37⋊C3)⋊(C33×C9) |
| Fitting, socle | C34×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C34×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | #66526 |
| commutator, hypocenter | C37 | C34×C9 |
| Frattini | C1 | G |
| Fitting, socle | C34×C37 | C9 |
| prime radical | C34×C37⋊C3 | C3 |
| cosocle | C37⋊C3 | C35 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C34 | |
10232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2997 |
1053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4428);