Finite Group DatabasebetaFinite Group Databasebeta| order | 26052 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊AGL(1,𝔽13) |
| unambiguous semidirect product | (C167⋊#261)⋊C3 |
| Fitting, socle, derived, Hall | C13×C167 ⋊ C3×C4 |
| Hall | C167⋊#261 ⋊ C3 |
| Hall | C13⋊C3×C167 ⋊ C4 |
| Sylow | C167 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ Dic167 |
| Sylow | C13 ⋊ C3×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C167 | C3×C4 |
| prime radical | D13⋊C3×C167 | C2 |
| cosocle | D13×C167 | C2×C3 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2171 |
Polycyclic presentation:
2,3,2,13,167|a^2=c,d^a=d^5,e^a=e^166,d^b=d^3,d^c=d^12677 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26052, 15);