Finite Group DatabasebetaFinite Group Databasebeta| order | 7758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D431 |
| unambiguous semidirect product | C431⋊(C2×C9) |
| Fitting, Hall | C9×C431 ⋊ C2 |
| derived, Sylow | C431 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D431 |
| commutator, hypocenter | C431 | C2×C9 |
| Frattini | C3 | C3×D431 |
| Fitting | C9×C431 | C2 |
| socle | C3×C431 | C2×C3 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
1953 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D431, C2×C9×D431 |
| maximal normal subgroup of | D9×D431, C2×C9×D431 |
| maximal quotient of | C9×Dic431, C2×C9×D431 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7758, 3);