Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1411 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^58,d^c=dfg,e^d=eg394 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1411, C2×#21422264, #28509018, … |
| maximal normal subgroup of | D59×#1411, C2×#21422264, #28509018, … |
| maximal quotient of | #28476073, #28476103, #28476204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2678);