Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C89⋊#64423 |
| Fitting, socle, derived, Hall | C72×C89 ⋊ C2×C3 |
| Hall | C89×#3861 ⋊ C2 |
| Hall | C7×D623 ⋊ C3 |
| Hall | #3861 ⋊ D89 |
| Sylow | C89 ⋊ #64423 |
| Sylow | C72 ⋊ C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C89 | C2×C3 |
| LCS | G ▷ C72×C89 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1246 |
Polycyclic presentation:
2,3,7^2,89|c^a=c^6,e^a=e^88,c^b=c^2,d^b=d^2853 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 27);