Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #427×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2234 |
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=g,c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^82,e^c=ef,f^c=fg1177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2234×D83, C2×#24909654, #35559203, … |
| maximal normal subgroup of | #2234×D83, C2×#24909654, #35559203, … |
| maximal quotient of | #35320701, #35320914, #35321347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6701);