Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #448×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3196 |
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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=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 | #35378564, #35378566, #35378632, … |
| maximal normal subgroup of | #35378564, #35378566, #35378632, … |
| maximal quotient of | #35413482, #35413491, #35414692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15337);