Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #1676 |
144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^78,e^c=eg1589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34202161, #34202163, #34202168, … |
| maximal normal subgroup of | #34202161, #34202163, #34202168, … |
| maximal quotient of | #34181328, #34184415, #34186631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3914);