Finite Group DatabasebetaFinite Group Databasebeta| order | 31684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C89 · Schur multiplier (H2) = C2 |
| direct product | C2×C89×D89 |
| unambiguous semidirect product | C89⋊(C22×C89) |
| unambiguous semidirect product | (C2×C89)⋊(C2×C89) |
| Fitting, socle | C2×C892 ⋊ C2 |
| derived | C89 ⋊ C22×C89 |
| Sylow | C892 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | D89 |
| commutator, cosocle, hypocenter | C89 | C22×C89 |
| Frattini | C1 | G |
| Fitting, socle | C2×C892 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C89 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 356 |
8188 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31684, 15);