Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C47 ⋊ C2 |
| Sylow | C47 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^5,47|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^46172 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D47, C2×#13094053, #15689919, … |
| maximal normal subgroup of | #137×D47, C2×#13094053, #15689919, … |
| maximal quotient of | #15689121, #15689130, #15689162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 175);