Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 53 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,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^82,d^b=df,f^b=fg,e^c=eg925 conjugacy classes — view the full character table.
| maximal subgroup of | #2195×D83, C2×#24909441, #35558357, … |
| maximal normal subgroup of | #2195×D83, C2×#24909441, #35558357, … |
| maximal quotient of | #35316557, #35316563, #35316901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6488);