Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #405×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2875 |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^82,d^c=dg,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319477, #35402982, #35402983, … |
| maximal normal subgroup of | #35319477, #35402982, #35402983, … |
| maximal quotient of | #35369996, #35369998, #35370015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12937);