Finite Group DatabasebetaFinite Group Databasebeta| order | 9052 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#64408 |
| Fitting, socle, derived, Hall | C31×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic31 |
| Sylow | C31 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C73 | C4 |
| LCS | G ▷ C31×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,31,73|a^2=b,c^a=c^30,d^a=d^27,d^b=d^72592 conjugacy classes — view the full character table.
| maximal subgroup of | #41029853, #41029854, (C31⋊C3)⋊#64408, … |
| maximal normal subgroup of | #41029853, #41029854, (C31⋊C3)⋊#64408, … |
| maximal quotient of | C3×C31⋊#64408, C3⋊(C31⋊#64408) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9052, 7);