Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #497×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3181 |
366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^78,d^c=dg,h^d=h^78656 conjugacy classes — view the full character table.
| maximal subgroup of | #34269639, #34269641, #34269669, … |
| maximal normal subgroup of | #34269639, #34269641, #34269669, … |
| maximal quotient of | #34288858, #34292594, #34292605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15216);