Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^d=h^82,h^e=h^821462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410275, #35410281, #35410286, … |
| maximal normal subgroup of | #35410275, #35410281, #35410286, … |
| maximal quotient of | #35562636, #35562638, #35562642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17716);