Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^a=bd,c^a=ce,f^a=fg,h^a=h^82,e^b=efg,d^c=df,h^c=h^82,e^d=eg553 conjugacy classes — view the full character table.
| maximal subgroup of | #2196×D83, C2×#24909448, #35558424, … |
| maximal normal subgroup of | #2196×D83, C2×#24909448, #35558424, … |
| maximal quotient of | #35316434, #35316435, #35316468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6495);