Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C81 · Schur multiplier (H2) = C9 |
| direct product | C81×#66526 |
| Fitting | C37×C81 ⋊ C9 |
| derived, Sylow | C37 ⋊ C9×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | #66526 |
| commutator, hypocenter | C37 | C9×C81 |
| Frattini | C27 | C3×#66526 |
| Fitting | C37×C81 | C9 |
| socle | C3×C37 | C9×C27 |
| prime radical | C3×C37⋊C3 | C3×C27 |
| cosocle | C27×C37⋊C3 | C32 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C81 | |
98 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, 4112);