Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3012 |
764 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^42,e^b=eg,d^c=dg746 conjugacy classes — view the full character table.
| maximal subgroup of | #25128047, #25128051, #25128071, … |
| maximal normal subgroup of | #25128047, #25128051, #25128071, … |
| maximal quotient of | #25069801, #25069834, #25069889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13814);