Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊((C13⋊C3)⋊D73) |
| unambiguous semidirect product | (C2×C3)⋊((C13⋊C3)⋊D73) |
| unambiguous semidirect product | (C2×C13⋊C3)⋊D219 |
| Fitting, socle | C2×C3×C13×C73 ⋊ C2×C3 |
| derived | C3×C13×C73 ⋊ C22×C3 |
| Hall | C3×C13⋊C3×C73 ⋊ C22 |
| Hall | C13×C73 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D73 |
| Sylow | C73 ⋊ C2×C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C2×C3×D219 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊((C13⋊C3)⋊D73) |
| commutator, cosocle, hypocenter | C3×C13×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C73 | C2×C3 |
| LCS | G ▷ C3×C13×C73 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5694 |
1542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 312);