Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C577 ⋊ C4 |
| Sylow | C577 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=d,b^a=bc,c^a=ce,f^a=f^553,d^b=de,f^d=f^5761163 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148849, #49148850, #49148851, … |
| maximal normal subgroup of | #49148849, #49148850, #49148851, … |
| maximal quotient of | #49148792, #49148795, #49148800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 204);