Finite Group DatabasebetaFinite Group Databasebeta| order | 17703 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C281⋊C7 |
| unambiguous semidirect product | C281⋊(C32×C7) |
| unambiguous semidirect product | (C3×C281)⋊(C3×C7) |
| unambiguous semidirect product | (C32×C281)⋊C7 |
| Fitting, socle, Hall | C32×C281 ⋊ C7 |
| derived, Sylow | C281 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C281⋊C7 |
| commutator, cosocle, hypocenter | C281 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C281 | C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2529 |
423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D281⋊C7, C3×C3⋊(D281⋊C7), C3×D3×C281⋊C7, … |
| maximal normal subgroup of | C32×D281⋊C7, C3×C3⋊(D281⋊C7), C3×D3×C281⋊C7, … |
| maximal quotient of | C2×C32×C281⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17703, 5);