Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2381 |
424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^82,c^b=cef,d^b=de1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301944, #35301947, #35301949, … |
| maximal normal subgroup of | #35301944, #35301947, #35301949, … |
| maximal quotient of | #35326031, #35326054, #35326058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7691);