Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#31822420 |
| Fitting | C2×C49×C61 ⋊ C2×C3 |
| derived, Hall | C49×C61 ⋊ C22×C3 |
| Hall | C2×C61×D49 ⋊ C3 |
| Hall | #22582217 ⋊ C22 |
| Hall | C2×D49 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C2×D49⋊C3 |
| Sylow | C49 ⋊ C22×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31822420 |
| commutator, cosocle, hypocenter | C49×C61 | C22×C3 |
| Frattini | C7 | C2×#14579425 |
| Fitting | C2×C49×C61 | C2×C3 |
| socle | C2×C7×C61 | AGL(1,𝔽7) |
| LCS | G ▷ C49×C61 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5978 |
1068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 42);