Finite Group DatabasebetaFinite Group Databasebeta| order | 9525 |
| isoclinism | isoclinic class of C127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C127⋊C3 |
| unambiguous semidirect product | C127⋊(C3×C52) |
| unambiguous semidirect product | (C5×C127)⋊(C3×C5) |
| Fitting, socle, Hall | C52×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
1125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9525, 6);