Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2162 |
160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,h^b=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#13050573, #35313417, #35313420, … |
| maximal normal subgroup of | C16×#13050573, #35313417, #35313420, … |
| maximal quotient of | #35319402, C4×(C2×D83)⋊C16, C4×Dic83⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6307);