Finite Group DatabasebetaFinite Group Databasebeta| order | 35028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#22576805 |
| derived, Hall | C7×C139 ⋊ C22×C9 |
| Hall | C22×C7×C139 ⋊ C9 |
| Hall | C22×C139 ⋊ C7⋊C9 |
| Sylow | C139 ⋊ C22×C7⋊C9 |
| Hall | C22×C7 ⋊ C139⋊C9 |
| Sylow | C7 ⋊ C22×C139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #15668589 |
| commutator, hypocenter | C7×C139 | C22×C9 |
| Frattini | C3 | C22×#15668589 |
| Fitting, socle, prime radical | C22×C3×C7×C139 | C3 |
| cosocle | C3×C7×C139 | C22×C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 35028 |
3924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35028, 55);