Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C61 · Schur multiplier (H2) = C2 |
| direct product | C61×#64422⋊C2 |
| unambiguous semidirect product | #64422⋊(C2×C61) |
| Fitting, socle, Hall | C72×C61 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C61 |
| Hall | D72×C61 ⋊ C3 |
| Hall | C61×#3862 ⋊ C22 |
| Hall | D72 ⋊ C3×C61 |
| Hall | #3862 ⋊ C22×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | #64422⋊C2 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C72×C61 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C61 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2562 |
1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 243);