Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #385×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×C4⋊C4 |
776 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,c^2=f,b^a=be,c^a=cf,d^b=de,h^c=h^82,h^d=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×C4⋊C4×D83, C2×#24910361, #35563717, … |
| maximal normal subgroup of | D4×C4⋊C4×D83, C2×#24910361, #35563717, … |
| maximal quotient of | #35325816, #35325818, #35325842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7408);