Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3394 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=eg,c^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^42,d^b=de,f^c=fg,h^d=h^42623 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3394, C2×#19147592, #25977538, … |
| maximal normal subgroup of | D43×#3394, C2×#19147592, #25977538, … |
| maximal quotient of | #25113394, #25113412, #25115431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17507);