Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1634 |
218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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=f,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^82,d^b=df,e^b=eg,d^c=dg,e^c=eg1051 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35325166, #1634×D83, C2×#24906608, … |
| maximal normal subgroup of | #35325166, #1634×D83, C2×#24906608, … |
| maximal quotient of | #35293237, #35293247, #35293421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3655);