Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2262 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,h^a=h^58,d^b=de,e^b=ef,f^b=fg,h^b=h^581894 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476572, #28476574, #28476575, … |
| maximal normal subgroup of | #28476572, #28476574, #28476575, … |
| maximal quotient of | #28509124, #28509192, C4×D1888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6819);