Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2274 |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35402201, #35402203, #35402205, … |
| maximal normal subgroup of | #35402201, #35402203, #35402205, … |
| maximal quotient of | #35325485, #35325488, #35325489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6864);