Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1722 |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #35292258, #35292260, #35317822, … |
| maximal normal subgroup of | #35292258, #35292260, #35317822, … |
| maximal quotient of | #35298191, #35304205, #35304208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4179);