Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #3069 |
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^78,d^b=dg,h^b=h^78,f^c=fg887 conjugacy classes — view the full character table.
| maximal subgroup of | #34325796, #34325797, #34325818, … |
| maximal normal subgroup of | #34325796, #34325797, #34325818, … |
| maximal quotient of | #34271050, #34271061, #34271094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14249);