Finite Group DatabasebetaFinite Group Databasebeta| order | 27269 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C67⋊C11 |
| unambiguous semidirect product | C67⋊(C11×C37) |
| unambiguous semidirect product | (C37×C67)⋊C11 |
| Fitting, socle, Hall | C37×C67 ⋊ C11 |
| derived, Sylow | C67 ⋊ C11×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C67⋊C11 |
| commutator, cosocle, hypocenter | C67 | C11×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2479 |
629 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27269, 1);