Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C571 ⋊ C2 |
| Sylow | C571 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=e,c^2=d,b^a=bd,f^b=f^5704580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49142220, #49142223, #49142281, … |
| maximal normal subgroup of | #49142220, #49142223, #49142281, … |
| maximal quotient of | #49142112, C4×(C2×D571)⋊C4, C4×Dic571⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 103);