Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊#1042 |
| derived, Hall | C52×C19 ⋊ C4×C9 |
| Hall | C52×#4294 ⋊ C4 |
| Hall | C19⋊#1042 ⋊ C9 |
| Hall | #4294 ⋊ #1042 |
| Sylow | C52 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C19⋊C3)⋊#1042 |
| commutator, hypocenter | C52×C19 | C4×C9 |
| Fitting, socle | C3×C52×C19 | C3×C4 |
| prime radical, cosocle | C3×C5×D5×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3420 |
Polycyclic presentation:
2,3,2,5^2,19,3|a^2=c,b^3=g,d^a=d^2,e^a=e^4,f^a=f^18,f^b=f^7,d^c=d^4297 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 178);