Finite Group DatabasebetaFinite Group Databasebeta| order | 26172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×C727⋊C9 |
| unambiguous semidirect product | (C4×C727)⋊C9 |
| derived, Sylow | C727 ⋊ C4×C9 |
| Hall | C4×C727 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C727⋊C3 |
| commutator, hypocenter | C727 | C4×C9 |
| Frattini | C2×C3 | C2×C727⋊C3 |
| Fitting | C3×C4×C727 | C3 |
| socle, prime radical, cosocle | C2×C3×C727 | C2×C3 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C3×C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26172 |
2940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26172, 3);