Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C43×#556 ⋊ C2 |
| Sylow | C43 ⋊ #3402 |
356 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^2=e,c^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^42554 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3402, C2×#19147670, #25977633, … |
| maximal normal subgroup of | D43×#3402, C2×#19147670, #25977633, … |
| maximal quotient of | #25113462, #25113468, #25115478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17585);