Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| derived, Hall | C52×C19 ⋊ C32×C4 |
| Hall | C19⋊C3×C52⋊C3 ⋊ C4 |
| Hall | C52×Dic19 ⋊ C32 |
| Hall | Dic19 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×C4×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C52⋊C3×D19⋊C3 |
| commutator, hypocenter | C52×C19 | C32×C4 |
| Fitting, socle, cosocle | C2×C52×C19 | C2×C32 |
| prime radical | C2×C19⋊C3×C52⋊C3 | C2 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1140 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 279);