Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3142 |
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=fg,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^78,d^b=dg,d^c=dg1592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34185902, #34189153, #34189155, … |
| maximal normal subgroup of | #34185902, #34189153, #34189155, … |
| maximal quotient of | #34288490, #34290977, #34291944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14911);