Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C47 ⋊ C2 |
| Sylow | C47 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 376 |
Polycyclic presentation:
2^5,47|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^46,d^b=de241 conjugacy classes — view the full character table.
| maximal subgroup of | #15689289, #15689290, #15689294, … |
| maximal normal subgroup of | #15689289, #15689290, #15689294, … |
| maximal quotient of | #15689122, #15689128, #15689163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 172);