Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | Dic19×C52⋊C9 |
| derived, Hall | C52×C19 ⋊ C4×C9 |
| Hall | C19×C52⋊C9 ⋊ C4 |
| Hall | C52×Dic19 ⋊ C9 |
| Sylow | C52 ⋊ C9×Dic19 |
| Sylow | C19 ⋊ C4×C52⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D19×C52⋊C3 |
| commutator, hypocenter | C52×C19 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3420 |
726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 78);