Finite Group DatabasebetaFinite Group Databasebeta| order | 10188 |
| automorphism | Aut(G) order 8619048 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5094 |
| direct product | C2×D2547 |
| unambiguous semidirect product | (C2×C9)⋊D283 |
| unambiguous semidirect product | (C2×C283)⋊D9 |
| Fitting | C2×C9×C283 ⋊ C2 |
| derived, Hall | C9×C283 ⋊ C22 |
| Sylow | C283 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D283 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2547 |
| commutator, cosocle, hypocenter | C9×C283 | C22 |
| Frattini | C3 | C2×D849 |
| Fitting | C2×C9×C283 | C2 |
| socle | C2×C3×C283 | D3 |
| LCS | G ▷ C9×C283 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D10188, C2×D7641, C2×D12735 |
| maximal normal subgroup of | D10188 |
| maximal quotient of | D10188, Dic5094, C2×D7641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10188, 15);