Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #427×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3076 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^82,f^c=fg,h^c=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35412232, #35412233, #35412243, … |
| maximal normal subgroup of | #35412232, #35412233, #35412243, … |
| maximal quotient of | #35403876, #35405346, #35405353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14296);