Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2435 |
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35302122, #35304830, #35304834, … |
| maximal normal subgroup of | #35302122, #35304830, #35304834, … |
| maximal quotient of | #35326396, #35326619, #35327214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8161);