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 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=f,c^2=f,e^2=g,b^a=bf,d^a=df,c^b=cf,h^c=h^82,h^e=h^821462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410297, #35410303, #35410308, … |
| maximal normal subgroup of | #35410297, #35410303, #35410308, … |
| maximal quotient of | #35562642, #35562645, #520×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17721);