Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C577 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^553,f^b=f^576,f^d=f^5761166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148863, #49148864, #49148877, … |
| maximal normal subgroup of | #49148863, #49148864, #49148877, … |
| maximal quotient of | #49148811, #49148812, #49148825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 217);