Finite Group DatabasebetaFinite Group Databasebeta| order | 27591 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C541⋊C3 |
| unambiguous semidirect product | C541⋊(C3×C17) |
| unambiguous semidirect product | (C17×C541)⋊C3 |
| Fitting, socle, Hall | C17×C541 ⋊ C3 |
| derived, Sylow | C541 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C541⋊C3 |
| commutator, cosocle, hypocenter | C541 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C541 | C3 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9197 |
3111 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27591, 1);