Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C5 |
| unambiguous semidirect product | (C22⋊(C19⋊C3))⋊(C52⋊C3) |
| unambiguous semidirect product | (C22⋊(C52⋊C3))⋊(C19⋊C3) |
| unambiguous semidirect product | (C19⋊(C52⋊C3))⋊A4 |
| Fitting, socle, derived, Hall | C22×C52×C19 ⋊ C32 |
| Hall | C52×C19 ⋊ C3×A4 |
| Hall | C22×C52 ⋊ C3×C19⋊C3 |
| Hall | C22×C19 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ A4×C19⋊C3 |
| Sylow | C19 ⋊ A4×C52⋊C3 |
| Sylow | C22 ⋊ C19⋊C3×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52×C19 | C32 |
| LCS | G ▷ C22×C52×C19 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1140 |
Polycyclic presentation:
3^2,2^2,5^2,19|e^a=e^3f^3,f^a=e^4f,g^a=g^7,c^b=d,d^b=cd,e^b=ef^2,f^b=ef^3260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 462);