Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #335×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1675 |
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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=fg,b^2=df,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^78,e^c=eg,h^c=h^781121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34202078, #34202080, #34202085, … |
| maximal normal subgroup of | #34202078, #34202080, #34202085, … |
| maximal quotient of | #34181324, #34184407, #34186625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3910);