Finite Group DatabasebetaFinite Group Databasebeta| order | 9228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C769⋊C3) |
| unambiguous semidirect product | C769⋊A4 |
| Fitting, socle, derived, Hall | C22×C769 ⋊ C3 |
| Sylow | C769 ⋊ A4 |
| Sylow | C22 ⋊ C769⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C769 | C3 |
| LCS | G ▷ C22×C769 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,769|b^a=c,c^a=bc,d^a=d^3601028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C769⋊C3, C3×C22⋊(C769⋊C3) |
| maximal normal subgroup of | A4×C769⋊C3, C3×C22⋊(C769⋊C3) |
| maximal quotient of | C22⋊(C769⋊C9), C3×C22⋊(C769⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9228, 13);