Finite Group DatabasebetaFinite Group Databasebeta| order | 31222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D233 |
| unambiguous semidirect product | C233⋊(C2×C67) |
| Fitting, socle, Hall | C67×C233 ⋊ C2 |
| derived, Sylow | C233 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D233 |
| commutator, cosocle, hypocenter | C233 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C67×C233 | C2 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C67 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15611 |
7906 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31222, 2);