Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1400 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1400×D83, C2×#24905602, #35324606, … |
| maximal normal subgroup of | #1400×D83, C2×#24905602, #35324606, … |
| maximal quotient of | #35291742, #35291802, #35291844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2649);