Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2983 |
356 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^82,c^b=ce1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298280, #35298283, #35298445, … |
| maximal normal subgroup of | #35298280, #35298283, #35298445, … |
| maximal quotient of | #35403140, #35403152, #35403452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13595);