Finite Group DatabasebetaFinite Group Databasebeta| order | 35028 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×#15668589 |
| Fitting, socle, derived, Hall | C22×C7×C139 ⋊ C32 |
| Hall | C7×C139 ⋊ C3×A4 |
| Hall | C22×C139 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C139 ⋊ A4×ΓL(1,𝔽8) |
| Hall | C22×C7 ⋊ C3×C139⋊C3 |
| Sylow | C7 ⋊ A4×C139⋊C3 |
| Sylow | C22 ⋊ C3×#15668589 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C7×C139 | C32 |
| LCS | G ▷ C22×C7×C139 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3892 |
1308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35028, 151);