Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#22555535 |
| Fitting, socle | C2×C52×C19 ⋊ C2×C9 |
| derived, Hall | C52×C19 ⋊ C22×C9 |
| Hall | C52⋊#4296 ⋊ C22 |
| Hall | C2×C5⋊D95 ⋊ C9 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽19) |
| Sylow | C19 ⋊ C2×(C5⋊D5)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22555535 |
| commutator, hypocenter | C52×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C19 | C2×C9 |
| prime radical | C2×C5⋊(C5⋊(D19⋊C3)) | C3 |
| cosocle | C52×C19⋊C3 | C22×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 365);