Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2123 |
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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=e,b^2=g,c^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^b=h^82,e^d=eg925 conjugacy classes — view the full character table.
| maximal subgroup of | #35319973, #35319974, #35319978, … |
| maximal normal subgroup of | #35319973, #35319974, #35319978, … |
| maximal quotient of | #35313499, #35313586, #35313670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6163);