Finite Group DatabasebetaFinite Group Databasebeta| order | 25404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×Dic87 |
| unambiguous semidirect product | C3⋊(C73×Dic29) |
| derived, Hall | C3×C29 ⋊ C4×C73 |
| Hall | C3×C29×C73 ⋊ C4 |
| Hall | C29×C73 ⋊ Dic3 |
| Hall | C3×C73 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic3×C73 |
| Sylow | C3 ⋊ C73×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | D87 |
| commutator, hypocenter | C3×C29 | C4×C73 |
| Frattini | C2 | C73×D87 |
| Fitting, socle, prime radical | C2×C3×C29×C73 | C2 |
| cosocle | C2×C3×C29 | C2×C73 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C2×C73 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25404 |
6570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25404, 8);