Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C3×D19⋊((C5⋊D5)⋊C3) |
| Fitting, socle | C3×C52×C19 ⋊ C22×C3 |
| derived, Hall | C52×C19 ⋊ C22×C32 |
| Hall | C3×C19⋊(C52⋊C3) ⋊ C22 |
| Hall | D19×C5⋊D5 ⋊ C32 |
| Sylow | C52 ⋊ C2×C3×D19⋊C3 |
| Sylow | C19 ⋊ C2×C3×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D19⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C22×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
160 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 160 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) = 855 |
186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 394);