Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| direct product | #737×C31⋊C3 |
| Fitting | C31×#737 ⋊ C3 |
| Sylow | C31 ⋊ C3×#737 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C32×C31⋊C3 |
| commutator, socle | C3×C31 | C34 |
| Frattini | C3 | C33×C31⋊C3 |
| Fitting | C31×#737 | C3 |
| hypercenter | #737 | C31⋊C3 |
| hypocenter | C31 | C3×#737 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C9 ◁ #737 | |
480 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6872, #36381048, #36381049, … |
| maximal normal subgroup of | C31⋊C3×#6872, #36381048, #36381049, … |
| maximal quotient of | C31⋊C3×#6887, C9×H(3,𝔽3)×C31⋊C3, C9×3−1+2×C31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 300);