Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C59×C22⋊C16 ⋊ C2 |
| Sylow | C59 ⋊ #2234 |
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=g,c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^58,e^c=ef,f^c=fg,h^c=h^581189 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2234, C2×#21426288, #28743490, … |
| maximal normal subgroup of | D59×#2234, C2×#21426288, #28743490, … |
| maximal quotient of | #28504987, #28505201, #28505630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6702);