Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #1728 |
480 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 221 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,e^2=g,b^a=bd,c^a=cg,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35290958, #35290979, #35290986, … |
| maximal normal subgroup of | #35290958, #35290979, #35290986, … |
| maximal quotient of | #35293786, #35293793, #35293797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4204);