Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C83⋊#1308 |
| Sylow | C83 ⋊ #1308 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1308×D83, C2×C83⋊#1308, #35294806, … |
| maximal normal subgroup of | #1308×D83, C2×C83⋊#1308, #35294806, … |
| maximal quotient of | #35290976, #35290977, #35290978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2422);