Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #520×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3046 |
472 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=dg,f^c=fg1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35442469, #35442474, #35442484, … |
| maximal normal subgroup of | #35442469, #35442474, #35442484, … |
| maximal quotient of | #35389870, #35389881, #35389892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14060);