Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C211⋊C9) |
| unambiguous semidirect product | C211⋊(C22⋊C9) |
| derived, Hall | C22×C211 ⋊ C9 |
| Sylow | C211 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C211⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C211⋊C3) |
| commutator, hypocenter | C22×C211 | C9 |
| Fitting, socle | C22×C3×C211 | C3 |
| LCS | G ▷ C22×C211 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,211,3|a^3=e,b^a=c,c^a=bc,d^a=d^14852 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊((C211⋊C5)⋊C9), C5×C22⋊(C211⋊C9) |
| maximal normal subgroup of | C22⋊((C211⋊C5)⋊C9), C5×C22⋊(C211⋊C9) |
| maximal quotient of | C5×C22⋊(C211⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 12);