Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#97×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1749 |
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,h^a=h^82,c^b=cg1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295869, #35295872, #35295875, … |
| maximal normal subgroup of | #35295869, #35295872, #35295875, … |
| maximal quotient of | #35294878, #35294889, #35294915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4273);