Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #454×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3018 |
724 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^82,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #35324653, #35324661, #35558565, … |
| maximal normal subgroup of | #35324653, #35324661, #35558565, … |
| maximal quotient of | #35376507, #35376564, #35376607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13857);