Finite Group DatabasebetaFinite Group Databasebeta| order | 22134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D527 |
| unambiguous semidirect product | C17⋊(C3×C7×D31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D527 |
| commutator, cosocle, hypocenter | C17×C31 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C31 | C2 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 ◁ C3×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11067 |
5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22134, 8);