Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Sylow | C31 ⋊ 3−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×C31⋊C3 |
| commutator, socle | C3×C31 | C34 |
| Fitting | C3×H(3,𝔽3)×C31 | C3 |
| hypercenter | C3×H(3,𝔽3) | C31⋊C3 |
| hypocenter | C31 | 3−1+4 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C3 ◁ C3×H(3,𝔽3) | |
460 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=e,b^a=be,d^a=de,f^a=f^25,c^b=ce413 conjugacy classes — view the full character table.
| maximal subgroup of | #36381334, #36381340, #36381343, … |
| maximal normal subgroup of | #36381334, #36381340, #36381343, … |
| maximal quotient of | #36382267, #36382271, #36382273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 308);