Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C571 ⋊ C2 |
| Sylow | C571 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|c^2=d,b^a=bd,c^a=ce,f^a=f^570,f^c=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142457, #123×D571, C2×#32912678, … |
| maximal normal subgroup of | #49142457, #123×D571, C2×#32912678, … |
| maximal quotient of | #49142127, #49142141, #49142143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 130);