Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #385×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2326 |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2326×D83, C2×#24910169, #35563209, … |
| maximal normal subgroup of | #2326×D83, C2×#24910169, #35563209, … |
| maximal quotient of | #35325662, #35325707, #35325717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7216);