Finite Group DatabasebetaFinite Group Databasebeta| order | 27753 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×C292⋊C3 |
| unambiguous semidirect product | C292⋊(C3×C11) |
| unambiguous semidirect product | (C11×C292)⋊C3 |
| Fitting, socle, Hall | C11×C292 ⋊ C3 |
| derived, Sylow | C292 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C292⋊C3 |
| commutator, cosocle, hypocenter | C292 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C292 | C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C11 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 957 |
3113 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27753, 3);