Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2187 |
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^82,d^b=df,f^b=fg1177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316504, #35316505, #35316509, … |
| maximal normal subgroup of | #35316504, #35316505, #35316509, … |
| maximal quotient of | #35316518, #35316862, #35317622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6439);