Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C571 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9136 |
Polycyclic presentation:
2^5,571|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^5702864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D571, C2×#32912671, #49142772, … |
| maximal normal subgroup of | C22⋊Q8×D571, C2×#32912671, #49142772, … |
| maximal quotient of | #49142124, #49142138, #49142141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 123);