Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2620 |
612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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=ef,d^2=e,b^a=be,c^a=cf,h^a=h^82,c^b=cg,d^c=de,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35442639, #35442640, #35442667, … |
| maximal normal subgroup of | #35442639, #35442640, #35442667, … |
| maximal quotient of | #35330777, #35330783, #35330804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 10272);