Finite Group DatabasebetaFinite Group Databasebeta| order | 26316 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C43⋊C3)⋊#595) |
| unambiguous semidirect product | (C43⋊C3)⋊(C3⋊#595) |
| unambiguous semidirect product | (C3⋊(C43⋊#595))⋊C3 |
| Fitting, socle, derived | C3×C17×C43 ⋊ C3×C4 |
| Hall | C3×C17×C43⋊C3 ⋊ C4 |
| Hall | C17×C43 ⋊ C3×Dic3 |
| Hall | C3×C43⋊C3 ⋊ #595 |
| Sylow | C43 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3⋊((C43⋊C3)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C43 | C3×C4 |
| prime radical | C3×D17×C43⋊C3 | C2 |
| cosocle | C3×D17×C43 | C2×C3 |
| LCS | G ▷ C3×C17×C43 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2193 |
Polycyclic presentation:
2,3,2,3,17,43|a^2=c,d^a=d^2,e^a=e^13,f^a=f^42,f^b=f^36,e^c=e^16264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26316, 66);