Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ #1422 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291848, #35291849, #35291851, … |
| maximal normal subgroup of | #35291848, #35291849, #35291851, … |
| maximal quotient of | #35292070, #35292077, #35292095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2708);