Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | Aut(G) order 8489664 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5202 |
| direct product | C2×D2601 |
| unambiguous semidirect product | (C2×C9)⋊D289 |
| unambiguous semidirect product | (C2×C289)⋊D9 |
| Fitting | C2×C9×C289 ⋊ C2 |
| derived, Hall | C9×C289 ⋊ C22 |
| Sylow | C289 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2601 |
| commutator, cosocle, hypocenter | C9×C289 | C22 |
| Frattini | C3×C17 | C2×D51 |
| Fitting | C2×C9×C289 | C2 |
| socle | C2×C3×C17 | D51 |
| LCS | G ▷ C9×C289 | |
| UCS | C1 ◁ C2 | |
45 conjugacy classes of subgroups.
2604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D10404, C2×D7803, C2×D13005 |
| maximal normal subgroup of | D10404 |
| maximal quotient of | D10404, Dic5202, C2×D7803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 12);