Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1307 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^82,c^b=cg,d^b=df,h^b=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291950, #35291951, #35292028, … |
| maximal normal subgroup of | #35291950, #35291951, #35292028, … |
| maximal quotient of | #35290978, #35290980, #35290996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2421);