Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3178 |
350 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,c^b=cg,d^b=dg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3178×D83, C2×#24918135, #36274296, … |
| maximal normal subgroup of | #3178×D83, C2×#24918135, #36274296, … |
| maximal quotient of | #35404987, #35408694, #35408706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15182);