Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1384 |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^82,d^b=dg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291971, #35291972, #35291974, … |
| maximal normal subgroup of | #35291971, #35291972, #35291974, … |
| maximal quotient of | #35291280, #35291328, #35291444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2612);