Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1778 |
220 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^b=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28503987, #28503989, #28504116, … |
| maximal normal subgroup of | #28503987, #28503989, #28504116, … |
| maximal quotient of | #28479886, #28479891, #28479896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4416);