Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C3×C27×C31⋊C3 |
| Fitting | C3×C27×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C31⋊C3 |
| commutator, hypocenter | C31 | C32×C27 |
| Frattini | C9 | C32×C31⋊C3 |
| Fitting | C3×C27×C31 | C3 |
| socle | C32×C31 | C3×C9 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C27 | |
144 conjugacy classes of subgroups.
1053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C3×C31⋊C3)⋊C81, #36379696, C9×C27×C31⋊C3, … |
| maximal normal subgroup of | (C3×C31⋊C3)⋊C81, #36379696, C9×C27×C31⋊C3, … |
| maximal quotient of | C9×C27×C31⋊C3, C3×C27×C31⋊C9, C31⋊C3×C32⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 234);