Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2472 |
786 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg,h^b=h^82,h^c=h^82,h^d=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2472×D83, C2×#24911596, #35572190, … |
| maximal normal subgroup of | #2472×D83, C2×#24911596, #35572190, … |
| maximal quotient of | #35326325, #35326558, #35327396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8643);