Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1554 |
198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^82,d^b=dg,e^b=efg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296752, #35296753, #35296817, … |
| maximal normal subgroup of | #35296752, #35296753, #35296817, … |
| maximal quotient of | #35292431, #35292441, #35292557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3220);