Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D571)⋊C8 |
| Fitting | C2×C8×C571 ⋊ C2 |
| Sylow | C571 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=d,d^2=e,b^a=bc,f^b=f^5704580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D571, C2×(C2×D571)⋊C8, #49142228, … |
| maximal normal subgroup of | C22⋊C8×D571, C2×(C2×D571)⋊C8, #49142228, … |
| maximal quotient of | #49141989, #49141991, #49141993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 58);