Finite Group DatabasebetaFinite Group Databasebeta| order | 15417 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C571⋊C3 |
| unambiguous semidirect product | C571⋊C33 |
| unambiguous semidirect product | (C3×C571)⋊C32 |
| Fitting, socle | C32×C571 ⋊ C3 |
| derived, Sylow | C571 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C571⋊C3 |
| commutator, cosocle, hypocenter | C571 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C571 | C3 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5139 |
1737 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15417, 13);