Finite Group DatabasebetaFinite Group Databasebeta| order | 35550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×#90646 |
| derived, Hall | C52⋊C9 ⋊ C2×C79 |
| Hall | C79×C52⋊C9 ⋊ C2 |
| Hall | C52×C79 ⋊ D9 |
| Sylow | C52 ⋊ D9×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | #90646 |
| commutator, cosocle, hypocenter | C52⋊C9 | C2×C79 |
| Frattini | C3 | C79×#3874 |
| Fitting, socle | C3×C52×C79 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C79 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3555 |
1896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35550, 39);