Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C73 · Schur multiplier (H2) = C2 |
| Fitting, socle | C3×C13×C73 ⋊ C22×C3 |
| derived | C3×C13 ⋊ C22×C3×C73 |
| Hall | C3×C13⋊C3×C73 ⋊ C22 |
| Hall | C13×C73 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C22×C73 |
| Sylow | C13 ⋊ C2×C3×D3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D3×D13⋊C3 |
| commutator, cosocle, hypocenter | C3×C13 | C22×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C73 | C22×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C73 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2847 |
1752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 250);