Finite Group DatabasebetaFinite Group Databasebeta| order | 33356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#11761640 |
| Fitting, socle, derived, Hall | C31×C269 ⋊ C4 |
| Sylow | C269 ⋊ Dic31 |
| Sylow | C31 ⋊ #11761640 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C269 | C4 |
| prime radical, cosocle | C31×D269 | C2 |
| LCS | G ▷ C31×C269 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8339 |
Polycyclic presentation:
2^2,31,269|a^2=b,c^a=c^30,d^a=d^82,d^b=d^2682111 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33356, 7);