Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #2165 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^58,e^b=eg,e^c=eg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475749, #28475750, #28475752, … |
| maximal normal subgroup of | #28475749, #28475750, #28475752, … |
| maximal quotient of | #28503705, #28503755, #28504023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6322);