Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#17987239 |
| Fitting | C4×C577 ⋊ C8 |
| Sylow | C577 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2308 |
Polycyclic presentation:
2^5,577|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^391,f^d=f^553,f^e=f^576308 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#17987239, Q8⋊#17987239, #49149038, … |
| maximal normal subgroup of | D4⋊#17987239, Q8⋊#17987239, #49149038, … |
| maximal quotient of | #49149038, #49149039, (C2×#17987239)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 239);