Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C81×C31⋊C3 |
| Fitting | C31×C81 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C81 |
| Frattini | C27 | C3×C31⋊C3 |
| Fitting | C31×C81 | C3 |
| socle | C3×C31 | C3×C27 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C81 | |
36 conjugacy classes of subgroups.
1053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31⋊C3×C243, #36379808, #36379809, … |
| maximal normal subgroup of | C31⋊C3×C243, #36379808, #36379809, … |
| maximal quotient of | C81×C31⋊C9, (C3×C31⋊C3)⋊C81, (C31⋊C9)⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 124);