Finite Group DatabasebetaFinite Group Databasebeta| order | 33573 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C31×C361 ⋊ C3 |
| Sylow | C361 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C361 | C3 |
| Frattini | C19 | #13183715 |
| socle | C19×C31 | C19⋊C3 |
| LCS | G ▷ C31×C361 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11191 |
Polycyclic presentation:
3,19,31,19|b^19=d^13,b^a=b^11d,c^a=c^5,d^a=d^113733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33573, 5);