Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C571 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #108×D571, C2×#32912629, #49142313, … |
| maximal normal subgroup of | #108×D571, C2×#32912629, #49142313, … |
| maximal quotient of | #49142016, #49142018, #49142030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 81);