Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊(D71⋊C7) |
| unambiguous semidirect product | ((C3⋊D3)⋊D71)⋊C7 |
| unambiguous semidirect product | (C3⋊(D71⋊C7))⋊D3 |
| Fitting, socle, derived, Hall | C32×C71 ⋊ C22×C7 |
| Hall | C32×C71⋊C7 ⋊ C22 |
| Hall | (C3⋊D3)⋊D71 ⋊ C7 |
| Hall | C71⋊C7 ⋊ D32 |
| Sylow | C71 ⋊ D32×C7 |
| Sylow | C32 ⋊ C2×D71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C71 | C22×C7 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 426 |
Polycyclic presentation:
2^2,7,3^2,71|e^a=e^2,f^a=f^70,d^b=d^2,e^b=e^2,f^c=f^4593 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 75);