Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#323 ⋊ C2 |
| Sylow | C59 ⋊ #1316 |
294 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,d^2=f,b^a=bc,c^a=ce,e^a=eg,d^b=de,h^b=h^58,d^c=dg664 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1316, C2×#21422023, #28497773, … |
| maximal normal subgroup of | D59×#1316, C2×#21422023, #28497773, … |
| maximal quotient of | #28475307, #28475315, #28475434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2437);