Finite Group DatabasebetaFinite Group Databasebeta| order | 35076 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C79⋊C3)⋊#3866 |
| Fitting, socle, derived, Hall | C37×C79 ⋊ C3×C4 |
| Hall | C79⋊#3866 ⋊ C3 |
| Hall | C37×C79⋊C3 ⋊ C4 |
| Hall | C79⋊C3 ⋊ #3866 |
| Sylow | C79 ⋊ C3×#3866 |
| Sylow | C37 ⋊ (C79⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C79 | C3×C4 |
| prime radical | D37×C79⋊C3 | C2 |
| cosocle | D37×C79 | C2×C3 |
| LCS | G ▷ C37×C79 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2923 |
Polycyclic presentation:
2,3,2,37,79|a^2=c,d^a=d^31,e^a=e^78,e^b=e^23,d^c=d^36299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35076, 35);