Finite Group DatabasebetaFinite Group Databasebeta| order | 26172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic727⋊C9 |
| unambiguous semidirect product | (C727⋊C9)⋊C4 |
| derived, Sylow | C727 ⋊ C4×C9 |
| Hall | C727⋊C9 ⋊ C4 |
| Hall | Dic727 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D727⋊C3 |
| commutator, hypocenter | C727 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C727 | C2×C3 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26172 |
Polycyclic presentation:
2,3,727,2,3|a^2=d,b^3=e,c^a=c^726,c^b=c^445762 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26172, 2);