Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊#26046024 |
| Fitting, socle, derived, Hall | C3×C72×C61 ⋊ C4 |
| Hall | C72×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ #5997 |
| Hall | C3×C72 ⋊ Dic61 |
| Sylow | C61 ⋊ C3⋊#5997 |
| Sylow | C72 ⋊ Dic183 |
| Sylow | C3 ⋊ #26046024 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C61 | C4 |
| prime radical, cosocle | C3×C61×C7⋊D7 | C2 |
| LCS | G ▷ C3×C72×C61 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2562 |
Polycyclic presentation:
2^2,3,7^2,61|a^2=b,c^a=c^2,d^a=d^4e^3,e^a=d^6e^3,f^a=f^60,d^b=d^6,e^b=e^62382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 326);