Finite Group DatabasebetaFinite Group Databasebeta| order | 26522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D149 |
| unambiguous semidirect product | C149⋊(C2×C89) |
| Fitting, socle, Hall | C89×C149 ⋊ C2 |
| derived, Sylow | C149 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D149 |
| commutator, cosocle, hypocenter | C149 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C89×C149 | C2 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C89 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13261 |
6764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26522, 2);