Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2576 |
468 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=efg,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2576×D83, C2×#24912767, #35574889, … |
| maximal normal subgroup of | #2576×D83, C2×#24912767, #35574889, … |
| maximal quotient of | #35326749, #35327010, #35327367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9814);