Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #490×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3136 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^78,h^c=h^78,h^d=h^78656 conjugacy classes — view the full character table.
| maximal subgroup of | #3136×D79, C2×#23773755, #35157523, … |
| maximal normal subgroup of | #3136×D79, C2×#23773755, #35157523, … |
| maximal quotient of | #34288474, #34290918, #34290934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14865);