Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2925 |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=e,f^2=g,b^a=be,d^b=dg,h^b=h^82,d^c=dg,h^c=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298710, #35298714, #35298724, … |
| maximal normal subgroup of | #35298710, #35298714, #35298724, … |
| maximal quotient of | #35401898, #35401955, #35402328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13175);