Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×#10596873 |
| derived, Sylow | C72 ⋊ C3×C4×C61 |
| Hall | C7×Dic7×C61 ⋊ C3 |
| Hall | C61×#3861 ⋊ C4 |
| Hall | C72×C61 ⋊ C3×C4 |
| Hall | C7×Dic7 ⋊ C3×C61 |
| Hall | #3861 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | #64423 |
| commutator, hypocenter | C72 | C3×C4×C61 |
| Frattini | C2 | C61×#64423 |
| Fitting, socle | C2×C72×C61 | C2×C3 |
| prime radical | C2×C61×#3861 | C2 |
| cosocle | C2×C72 | C2×C3×C61 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C61 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1708 |
2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 100);