Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×M16×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,h^a=h^82,e^b=eg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309865, #35309871, #35309897, … |
| maximal normal subgroup of | #35309865, #35309871, #35309897, … |
| maximal quotient of | #35370780, #35370840, #35370859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13030);