Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316169, #35316173, #35316183, … |
| maximal normal subgroup of | #35316169, #35316173, #35316183, … |
| maximal quotient of | #35319745, #35319749, #35322016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6412);