Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #423×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^b=h^82,d^c=dg,h^c=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298729, #35298733, #35298743, … |
| maximal normal subgroup of | #35298729, #35298733, #35298743, … |
| maximal quotient of | #35375825, #35375833, #35375842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13245);