Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2962 |
356 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,h^a=h^82,d^c=dg1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298884, #35298888, #35298898, … |
| maximal normal subgroup of | #35298884, #35298888, #35298898, … |
| maximal quotient of | #35402386, #35402403, #35403047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13457);