Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C37 |
| direct product | C32×C32⋊(C79⋊C3) |
| Fitting | C34×C79 ⋊ C3 |
| Sylow | C79 ⋊ C32×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C3×C79⋊C3 |
| commutator, cosocle | C3×C79 | C34 |
| Frattini | C3 | C33×C79⋊C3 |
| Fitting | C34×C79 | C3 |
| socle | C33×C79 | C32 |
| hypercenter | C34 | C79⋊C3 |
| hypocenter | C79 | C32×H(3,𝔽3) |
| LCS | G ▷ C3×C79 ▷ C79 | |
| UCS | C1 ◁ C33 ◁ C34 | |
900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6399 |
2205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 295);