Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2161 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^82,c^b=cg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319831, #35319836, #35320931, … |
| maximal normal subgroup of | #35319831, #35319836, #35320931, … |
| maximal quotient of | #35315993, #35316057, #35316085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6305);