Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C83 ⋊ #1453 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cg,h^a=h^82,c^b=cf,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291467, #35291469, #35314487, … |
| maximal normal subgroup of | #35291467, #35291469, #35314487, … |
| maximal quotient of | #35293774, #35293793, #35294837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2807);