Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10597845⋊C9 |
| derived, Sylow | C157 ⋊ C4×C9 |
| Hall | C157⋊C9 ⋊ C4 |
| Hall | #10597845 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10597845⋊C3 |
| commutator, hypocenter | C157 | C4×C9 |
| Fitting, socle | C3×C157 | C3×C4 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,157,3|a^2=c,b^3=e,d^a=d^28,d^b=d^12,d^c=d^15675 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#10597845⋊C9, #15691169⋊C9, #15691170⋊C9, … |
| maximal normal subgroup of | C5×#10597845⋊C9 |
| maximal quotient of | C5×#10597845⋊C9, #15691169⋊C9, #15691170⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 8);