Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3021 |
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #35435809, #35435812, #35435831, … |
| maximal normal subgroup of | #35435809, #35435812, #35435831, … |
| maximal quotient of | #35376795, #35376842, #35376873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13879);