Finite Group DatabasebetaFinite Group Databasebeta| order | 27225 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C121 · Schur multiplier (H2) = C5 |
| direct product | C121×C52⋊C9 |
| unambiguous semidirect product | C52⋊(C9×C121) |
| unambiguous semidirect product | (C52×C121)⋊C9 |
| derived, Sylow | C52 ⋊ C9×C121 |
| Hall | C52×C121 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C121 | C52⋊C3 |
| commutator, hypocenter | C52 | C9×C121 |
| Frattini | C3×C11 | C11×C52⋊C3 |
| Fitting | C3×C52×C121 | C3 |
| socle, prime radical, cosocle | C3×C52×C11 | C3×C11 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C121 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5445 |
3993 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27225, 7);