Finite Group DatabasebetaFinite Group Databasebeta| order | 33196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#11715871 |
| Fitting, socle, derived, Hall | C43×C193 ⋊ C4 |
| Sylow | C193 ⋊ Dic43 |
| Sylow | C43 ⋊ #11715871 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C193 | C4 |
| prime radical, cosocle | C43×D193 | C2 |
| LCS | G ▷ C43×C193 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8299 |
Polycyclic presentation:
2^2,43,193|a^2=b,c^a=c^42,d^a=d^81,d^b=d^1922110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33196, 7);