Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#137×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2007 |
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,e^c=eg,h^c=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2007, C2×#21425141, #28615653, … |
| maximal normal subgroup of | D59×#2007, C2×#21425141, #28615653, … |
| maximal quotient of | #28489022, #28489023, #28489029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5555);