Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C59 ⋊ #1426 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^58,d^b=dg,h^b=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1426, C2×#21422303, #28509208, … |
| maximal normal subgroup of | D59×#1426, C2×#21422303, #28509208, … |
| maximal quotient of | #28476371, #28476398, C2×#21422303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2717);