Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D577⋊M16 |
| Sylow | C577 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=d,d^2=e,b^a=be,f^a=f^553,f^c=f^576,f^d=f^5761172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148816, #49148818, #49148820, … |
| maximal normal subgroup of | #49148816, #49148818, #49148820, … |
| maximal quotient of | #49148908, C4×#22604427, C4×#22604428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 231);