Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2905 |
484 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=e,f^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35310446, #35310448, #35310449, … |
| maximal normal subgroup of | #35310446, #35310448, #35310449, … |
| maximal quotient of | #35373548, #35373552, #35373556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13073);