Finite Group DatabasebetaFinite Group Databasebeta| order | 33573 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C31⋊#11762246 |
| Fitting, socle, derived, Hall | C192×C31 ⋊ C3 |
| Sylow | C192 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ #11762246 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192×C31 | C3 |
| LCS | G ▷ C192×C31 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1767 |
Polycyclic presentation:
3,19^2,31|b^a=b^7,c^a=c^11,d^a=d^53733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33573, 15);