Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C31×C81 ⋊ C3 |
| Sylow | C31 ⋊ C81⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C27 | C3×C31⋊C3 |
| commutator, socle | C3×C31 | C3×C27 |
| Fitting | C31×C81 | C3 |
| hypercenter | C81 | C31⋊C3 |
| hypocenter | C31 | C81⋊C3 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C27 ◁ C81 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=c,c^3=d,d^3=e,b^a=be,f^b=f^5909 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×C81⋊C3, C3×#21419257, #36382066, … |
| maximal normal subgroup of | C31⋊C3×C81⋊C3, C3×#21419257, #36382066, … |
| maximal quotient of | #36379689, (C3×C31⋊C3)⋊C81, (C31⋊C9)⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 127);