Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C19⋊C3)⋊#1042 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×#1042) |
| unambiguous semidirect product | (C19⋊#1042)⋊C32 |
| unambiguous semidirect product | (C3×C19⋊#1042)⋊C3 |
| Fitting, socle | C3×C52×C19 ⋊ C3×C4 |
| derived, Hall | C52×C19 ⋊ C32×C4 |
| Hall | C3×C52×C19⋊C3 ⋊ C4 |
| Hall | C19⋊#1042 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ #1042 |
| Sylow | C52 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C32×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C19⋊C3)⋊#1042 |
| 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 | C5×D5×C19 | C2×C32 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1140 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 378);