Finite Group DatabasebetaFinite Group Databasebeta| order | 35836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C31⋊#11923884 |
| Fitting, socle, derived, Hall | C172×C31 ⋊ C4 |
| Sylow | C172 ⋊ Dic31 |
| Sylow | C31 ⋊ #11923884 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C172×C31 | C4 |
| prime radical, cosocle | C31×C17⋊D17 | C2 |
| LCS | G ▷ C172×C31 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1054 |
Polycyclic presentation:
2^2,17^2,31|a^2=b,c^a=c^13,d^a=d^4,e^a=e^30,c^b=c^16,d^b=d^162266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35836, 31);