Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#17987239 |
| unambiguous semidirect product | (C2×#17987239)⋊C2 |
| Fitting | C22×C577 ⋊ C8 |
| Sylow | C577 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2308 |
Polycyclic presentation:
2^5,577|a^2=d,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 | #49149034, #49149035, C2×C22⋊#17987239, … |
| maximal normal subgroup of | #49149034, #49149035, C2×C22⋊#17987239, … |
| maximal quotient of | #49149034, #49149035, D4⋊#17987239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 238);