Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2993 |
354 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,d^b=dg,h^b=h^82,h^c=h^82,h^d=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35374465, #35374469, #35374480, … |
| maximal normal subgroup of | #35374465, #35374469, #35374480, … |
| maximal quotient of | #35403225, #35403266, #35403360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13658);