Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #469×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^82,d^c=dg,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #35315396, #35315404, #35558304, … |
| maximal normal subgroup of | #35315396, #35315404, #35558304, … |
| maximal quotient of | #35387473, #35387512, #35387560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14156);