Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | Aut(G) order 8525088 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5382 |
| direct product | C2×D2691 |
| unambiguous semidirect product | (C2×C9)⋊D299 |
| unambiguous semidirect product | (C2×C13)⋊D207 |
| unambiguous semidirect product | (C2×C23)⋊D117 |
| Fitting | C2×C9×C13×C23 ⋊ C2 |
| derived, Hall | C9×C13×C23 ⋊ C22 |
| Hall | C13×C23 ⋊ C2×D9 |
| Hall | C9×C23 ⋊ C2×D13 |
| Hall | C9×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D117 |
| Sylow | C13 ⋊ C2×D207 |
| Sylow | C9 ⋊ C2×D299 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2691 |
| commutator, cosocle, hypocenter | C9×C13×C23 | C22 |
| Frattini | C3 | C2×D897 |
| Fitting | C2×C9×C13×C23 | C2 |
| socle | C2×C3×C13×C23 | D3 |
| LCS | G ▷ C9×C13×C23 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
2694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D10764, C2×D8073, C2×D13455 |
| maximal normal subgroup of | D10764 |
| maximal quotient of | D10764, Dic5382, C2×D8073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 40);