Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2101 |
198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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=dg,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^78,c^b=cf,f^b=fg,f^c=fg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2101×D79, C2×#23764971, #34318181, … |
| maximal normal subgroup of | #2101×D79, C2×#23764971, #34318181, … |
| maximal quotient of | #34193407, #34196183, #34196534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6081);