Finite Group DatabasebetaFinite Group Databasebeta| order | 29726 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | C167×D89 |
| unambiguous semidirect product | C89⋊(C2×C167) |
| Fitting, socle, Hall | C89×C167 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D89 |
| commutator, cosocle, hypocenter | C89 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C89×C167 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14863 |
7682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29726, 1);