Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| unambiguous semidirect product | C79⋊H(5,𝔽3) |
| Fitting | C3×H(3,𝔽3)×C79 ⋊ C3 |
| Sylow | C79 ⋊ H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×C79⋊C3 |
| commutator, socle, cosocle | C3×C79 | C34 |
| Fitting | C3×H(3,𝔽3)×C79 | C3 |
| hypercenter | C3×H(3,𝔽3) | C79⋊C3 |
| hypocenter | C79 | H(5,𝔽3) |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C3 ◁ C3×H(3,𝔽3) | |
586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2133 |
Polycyclic presentation:
3^5,79|b^a=be,d^a=de,c^b=ce,f^d=f^23941 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 304);