Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2982 |
396 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^82,c^b=ce1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298270, #35298273, #35299052, … |
| maximal normal subgroup of | #35298270, #35298273, #35299052, … |
| maximal quotient of | #35403135, #35403444, #35413815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13591);