Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14556313)⋊C4 |
| Fitting | C2×C4×C577 ⋊ C4 |
| Sylow | C577 ⋊ #95 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=d,b^2=e,b^a=bc,f^a=f^553,f^d=f^5761172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148800, #49148801, #49148802, … |
| maximal normal subgroup of | #49148800, #49148801, #49148802, … |
| maximal quotient of | #49148814, #49148815, #49148816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 197);