Finite Group DatabasebetaFinite Group Databasebeta| order | 33222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×D7×C113⋊C7 |
| unambiguous semidirect product | (C3×D7×C113)⋊C7 |
| Fitting, socle | C3×C7×C113 ⋊ C2×C7 |
| derived | C7×C113 ⋊ C2×C3×C7 |
| Hall | C3×C7×C113⋊C7 ⋊ C2 |
| Hall | C7×C113⋊C7 ⋊ C2×C3 |
| Hall | C3×C113 ⋊ C7×D7 |
| Sylow | C113 ⋊ C3×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×C113⋊C7 |
| commutator, cosocle, hypocenter | C7×C113 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C113 | C2×C7 |
| LCS | G ▷ C7×C113 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2373 |
345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33222, 24);