Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#123×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2849 |
1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1102 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|c^2=e,b^a=be,c^a=cf,d^a=dg,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35435988, #35435990, #35436001, … |
| maximal normal subgroup of | #35435988, #35435990, #35436001, … |
| maximal quotient of | #35335565, #35335611, #35335616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12799);