Finite Group DatabasebetaFinite Group Databasebeta| order | 25575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#22555294 |
| derived, Hall | C11×C31 ⋊ C3×C25 |
| Hall | C3×C11×C31 ⋊ C25 |
| Hall | C3×C31 ⋊ C11⋊C25 |
| Hall | C3×C11 ⋊ C31⋊C25 |
| Sylow | C31 ⋊ C3×C11⋊C25 |
| Sylow | C11 ⋊ C3×C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #13133724 |
| commutator, hypocenter | C11×C31 | C3×C25 |
| Frattini | C5 | C3×#13133724 |
| Fitting, socle, prime radical | C3×C5×C11×C31 | C5 |
| cosocle | C5×C11×C31 | C3×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25575 |
1095 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25575, 7);