Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C32×C31⋊C27 |
| derived, Sylow | C31 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | C31⋊C3 |
| commutator, hypocenter | C31 | C32×C27 |
| Frattini | C9 | C32×C31⋊C3 |
| Fitting | C32×C9×C31 | C3 |
| socle | C33×C31 | C9 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C9 | |
144 conjugacy classes of subgroups.
1053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36379495, H(3,𝔽3)⋊(C31⋊C27), #36379498, … |
| maximal normal subgroup of | #36379495, H(3,𝔽3)⋊(C31⋊C27), #36379498, … |
| maximal quotient of | C3×C9×C31⋊C27, C3×C32⋊(C31⋊C27), C3×#21419247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 235);