Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1574 |
158 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 158 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,b^2=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^82,c^b=cfg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298677, #35298678, #35298684, … |
| maximal normal subgroup of | #35298677, #35298678, #35298684, … |
| maximal quotient of | #35293892, #35295621, #35297260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3299);