Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2189 |
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 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=g,c^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 | #2189×D83, C2×#24909403, #35558179, … |
| maximal normal subgroup of | #2189×D83, C2×#24909403, #35558179, … |
| maximal quotient of | #35316529, #35316873, #35317633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6450);