Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2969 |
370 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^82,c^b=cg,d^c=dg1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35375314, #35375318, #35375351, … |
| maximal normal subgroup of | #35375314, #35375318, #35375351, … |
| maximal quotient of | #35402672, #35402707, #35402796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13514);