Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic1142 |
| Sylow | C571 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18272 |
4580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49141996, #49141998, C4×#22603721, … |
| maximal normal subgroup of | #49141996, #49141998, C4×#22603721, … |
| maximal quotient of | C4×C4⋊Dic571, C4×Dic571⋊C4, #49142149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 112);