Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D571 |
| Fitting | Q16×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×Q16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
2009 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D571, Q32×D571, #49142705, … |
| maximal normal subgroup of | SD32×D571, Q32×D571, #49142705, … |
| maximal quotient of | #103×D571, #107×D571, #49142358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 162);