Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #436×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3272 |
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,c^b=cg,d^b=de,e^b=eg,h^b=h^82,e^d=eg,h^d=h^821177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35393756, #35393758, #35393801, … |
| maximal normal subgroup of | #35393756, #35393758, #35393801, … |
| maximal quotient of | #35395673, #35395753, #35395870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16112);