Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 137 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=d,b^2=e,d^2=f,e^2=g,c^a=cf,h^a=h^82,h^b=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294961, #35294965, #35294966, … |
| maximal normal subgroup of | #35294961, #35294965, #35294966, … |
| maximal quotient of | #35293758, #35293787, #35294831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2791);