Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2087 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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=d,c^2=dg,e^2=g,b^a=bd,c^a=ce,c^b=cf,h^b=h^82,e^c=eg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35317682, #35317687, #35317692, … |
| maximal normal subgroup of | #35317682, #35317687, #35317692, … |
| maximal quotient of | #35309316, #35309326, #35309352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6004);