Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #417×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2896 |
772 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eg,h^c=h^82,h^d=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35403697, #35403699, #35403704, … |
| maximal normal subgroup of | #35403697, #35403699, #35403704, … |
| maximal quotient of | #35370776, #35370836, #35370855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13026);