Finite Group DatabasebetaFinite Group Databasebeta| order | 26172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C727⋊C3)⋊C4) |
| unambiguous semidirect product | (C727⋊C3)⋊Dic3 |
| unambiguous semidirect product | Dic2181⋊C3 |
| derived | C3×C727 ⋊ C3×C4 |
| Hall | C3×C727⋊C3 ⋊ C4 |
| Sylow | C727 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D727⋊C3) |
| commutator, hypocenter | C3×C727 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C727 | C2×C3 |
| prime radical | C2×C3×C727⋊C3 | C2 |
| LCS | G ▷ C3×C727 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8724 |
Polycyclic presentation:
2,3^2,727,2|a^2=e,c^a=c^2,d^a=d^726,d^b=d^445744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26172, 18);