Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C38 |
| unambiguous semidirect product | C31⋊#10624562 |
| Fitting | C32×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ #10624562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C31⋊C3 |
| commutator, socle, cosocle | C33×C31 | C33 |
| Fitting | C32×H(3,𝔽3)×C31 | C3 |
| hypercenter | C32×H(3,𝔽3) | C31⋊C3 |
| hypocenter | C31 | #10624562 |
| LCS | G ▷ C33×C31 ▷ C31 | |
| UCS | C1 ◁ C33 ◁ C32×H(3,𝔽3) | |
2138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7533 |
Polycyclic presentation:
3^6,31|b^a=bd,c^a=ce,c^b=cf,g^c=g^251095 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 951);