Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #493×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 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|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^82,h^c=h^82,e^d=eg,h^d=h^82937 conjugacy classes — view the full character table.
| maximal subgroup of | #35317825, #35317829, #35317853, … |
| maximal normal subgroup of | #35317825, #35317829, #35317853, … |
| maximal quotient of | #35393750, #35393765, #35393780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16185);