Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2008 |
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,h^b=h^82,d^c=dg,e^c=eg925 conjugacy classes — view the full character table.
| maximal subgroup of | #2008×D83, C2×#24908514, #35431409, … |
| maximal normal subgroup of | #2008×D83, C2×#24908514, #35431409, … |
| maximal quotient of | #35304710, #35304724, #35304738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5561);