Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2188 |
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 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,b^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 | #35316521, #35316522, #35316526, … |
| maximal normal subgroup of | #35316521, #35316522, #35316526, … |
| maximal quotient of | #35316523, #35316867, #35317627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6444);