Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#22603722 |
| Fitting | C2×C8×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
4574 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142353, C4×#22603722, #49142365, … |
| maximal normal subgroup of | #49142353, C4×#22603722, #49142365, … |
| maximal quotient of | C2×#32912616, C2×#32912619, C2×#32912626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 161);