Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #418×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2897 |
778 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,e^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^82,d^c=dg,h^c=h^82,h^d=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35420381, #35420385, #35420392, … |
| maximal normal subgroup of | #35420381, #35420385, #35420392, … |
| maximal quotient of | #35370785, #35370880, #35370882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13035);