Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C571 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4568 |
Polycyclic presentation:
2^5,571|a^2=d,b^a=bc,c^a=ce,f^a=f^570,d^b=de2861 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142053, #49142054, #49142056, … |
| maximal normal subgroup of | #49142053, #49142054, #49142056, … |
| maximal quotient of | #49141990, #49141992, #49142000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 61);