Finite Group DatabasebetaFinite Group Databasebeta| order | 22383 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C829 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #21418661 |
| commutator, hypocenter | C829 | C27 |
| Fitting, socle, prime radical | C3×C829 | C9 |
| cosocle | #21418659 | C3 |
| LCS | G ▷ C829 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22383 |
Polycyclic presentation:
3^3,829|a^3=b,b^3=c,d^a=d^5,d^b=d^125303 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22383, 14);