Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #2049 |
254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 254 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,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^c=fg,h^c=h^78881 conjugacy classes — view the full character table.
| maximal subgroup of | #2049×D79, C2×#23764677, #34316112, … |
| maximal normal subgroup of | #2049×D79, C2×#23764677, #34316112, … |
| maximal quotient of | #34191860, #34191867, #34191874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5787);