Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #491×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3139 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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,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,d^c=dg,h^c=h^78,h^d=h^78656 conjugacy classes — view the full character table.
| maximal subgroup of | #34199464, #34208630, #34269584, … |
| maximal normal subgroup of | #34199464, #34208630, #34269584, … |
| maximal quotient of | #34288482, #34290983, #34291948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14889);