Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #2046 |
276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^78,c^b=cf,d^b=dg,e^c=eg,f^c=fg884 conjugacy classes — view the full character table.
| maximal subgroup of | #2046×D79, C2×#23764661, #34316069, … |
| maximal normal subgroup of | #2046×D79, C2×#23764661, #34316069, … |
| maximal quotient of | #34191847, #34191854, #34191863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5771);