Finite Group DatabasebetaFinite Group Databasebeta| order | 38106 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C29×C73 ⋊ C2×C3 |
| derived, Hall | C29×C73 ⋊ C2×C32 |
| Hall | C3×C29×C73⋊C3 ⋊ C2 |
| Hall | D2117 ⋊ C32 |
| Hall | C3×C73⋊C3 ⋊ D29 |
| Sylow | C73 ⋊ C32×D29 |
| Sylow | C29 ⋊ C3×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C29⋊(D73⋊C3) |
| commutator, cosocle, hypocenter | C29×C73 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C73 | C2×C3 |
| LCS | G ▷ C29×C73 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6351 |
1188 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38106, 19);