Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C89⋊#64418 |
| Fitting, socle, Hall | C72×C89 ⋊ D3 |
| derived, Hall | C89×#3862 ⋊ C2 |
| Hall | #3862 ⋊ D89 |
| Sylow | C89 ⋊ #64418 |
| Sylow | C72 ⋊ D267 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C89×#3862 | C2 |
| Fitting, socle | C72×C89 | D3 |
| LCS | G ▷ C89×#3862 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1246 |
Polycyclic presentation:
2,3,89,7^2|b^a=b^2,c^a=c^88,d^a=d^4e,e^a=d^6e^3,d^b=d^2e^6,e^b=e^4856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 15);