Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C577 ⋊ C4 |
| Sylow | C577 ⋊ #106 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,f^a=f^553,f^d=f^5761166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148865, #49148866, #49148873, … |
| maximal normal subgroup of | #49148865, #49148866, #49148873, … |
| maximal quotient of | #49148810, #49148811, #49148823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 214);