Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×C22⋊(C61⋊C3) |
| unambiguous semidirect product | C22⋊(C72×C61⋊C3) |
| unambiguous semidirect product | C61⋊(C72×A4) |
| Fitting, socle, Hall | C22×C72×C61 ⋊ C3 |
| derived, Hall | C22×C61 ⋊ C3×C72 |
| Hall | C72×C61 ⋊ A4 |
| Hall | C22×C72 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C72×A4 |
| Sylow | C22 ⋊ C72×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C22⋊(C61⋊C3) |
| commutator, cosocle, hypocenter | C22×C61 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C61 | C3 |
| LCS | G ▷ C22×C61 | |
| UCS | C1 ◁ C72 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11956 |
4116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 349);