Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #450×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3193 |
462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^82,f^c=fg805 conjugacy classes — view the full character table.
| maximal subgroup of | #35378521, #35378535, #35378589, … |
| maximal normal subgroup of | #35378521, #35378535, #35378589, … |
| maximal quotient of | #35413452, #35413460, #35414683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15313);