Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊(#4294⋊C2))⋊D5 |
| derived, Hall | C52×C19 ⋊ C22×C9 |
| Hall | C52×#4294 ⋊ C22 |
| Hall | (C5⋊D5)⋊D19 ⋊ C9 |
| Hall | #4294 ⋊ D52 |
| Sylow | C52 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C9×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊(D19⋊C3))⋊D5 |
| commutator, hypocenter | C52×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C19 | C22×C3 |
| prime radical | C3×(C5⋊D5)⋊D19 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1710 |
Polycyclic presentation:
2^2,3,5^2,19,3|c^3=g,d^a=d^4,f^a=f^18,d^b=d^4,e^b=e^4,f^c=f^7270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 182);