Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1458 |
264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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=f,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35313487, #35313489, #35313495, … |
| maximal normal subgroup of | #35313487, #35313489, #35313495, … |
| maximal quotient of | #35292340, #35292348, #35292395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2821);