Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#19152831 |
| Fitting, socle | C3×C52×C19 ⋊ C3×C4 |
| derived, Hall | C52×C19 ⋊ C32×C4 |
| Hall | C3×C19⋊(C52⋊C3) ⋊ C4 |
| Hall | C19⋊#1043 ⋊ C32 |
| Sylow | C52 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×#1043⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19152831 |
| commutator, hypocenter | C52×C19 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C3×C4 |
| prime radical | C3×(C5⋊D5)⋊(C19⋊C3) | C2 |
| cosocle | C19×C5⋊D5 | C2×C32 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 389);