Finite Group DatabasebetaFinite Group Databasebeta| order | 9228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic769⋊C3 |
| derived, Sylow | C769 ⋊ C3×C4 |
| Hall | Dic769 ⋊ C3 |
| Hall | C769⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D769⋊C3 |
| commutator, hypocenter | C769 | C3×C4 |
| Fitting, socle | C2×C769 | C2×C3 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,769,2|a^2=d,c^a=c^768,c^b=c^360268 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic769⋊C3, C3⋊(Dic769⋊C3) |
| maximal normal subgroup of | C3×Dic769⋊C3 |
| maximal quotient of | Dic769⋊C9, C3×Dic769⋊C3, C3⋊(Dic769⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9228, 2);