Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #346×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1333 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^82,c^b=ceg,d^b=dg,e^b=eg,h^b=h^821672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1333×D83, C2×#24905431, #35314169, … |
| maximal normal subgroup of | #1333×D83, C2×#24905431, #35314169, … |
| maximal quotient of | #35291060, #35291072, #35291172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2478);