Finite Group DatabasebetaFinite Group Databasebeta| order | 20397 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C523 ⋊ C3 |
| Sylow | C523 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C523⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C523 | C3 |
| LCS | G ▷ C13×C523 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6799 |
Polycyclic presentation:
3,13,523|b^a=b^9,c^a=c^602269 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20397, 4);