Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C3×C31⋊C81 |
| unambiguous semidirect product | (C3×C31)⋊C81 |
| derived, Sylow | C31 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C81 |
| Frattini | C27 | C3×C31⋊C3 |
| Fitting | C3×C27×C31 | C3 |
| socle | C32×C31 | C27 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C27 | |
36 conjugacy classes of subgroups.
1053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C81×C31⋊C9, C9×C31⋊C81, #36379688, … |
| maximal normal subgroup of | C81×C31⋊C9, C9×C31⋊C81, #36379688, … |
| maximal quotient of | C9×C31⋊C81, C32⋊(C31⋊C81), #36379800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 125);