Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C36 |
No aliases for this group.
| Sylow | C31 ⋊ #10624547 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C31⋊C3 |
| commutator | C32×C31 | C32×C9 |
| Fitting, prime radical | C35×C31 | C3 |
| socle, cosocle | C33×C31 | C33 |
| hypercenter | C35 | C31⋊C3 |
| hypocenter | C31 | #10624547 |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C33 ◁ C35 | |
2150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2511 |
Polycyclic presentation:
3^6,31|a^3=f,b^a=bd,c^a=ce,g^a=g^252583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 869);