Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #2296 |
656 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 317 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=g,d^2=f,b^a=be,c^a=cf,h^a=h^78,h^b=h^781616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34181754, #34181757, #34194248, … |
| maximal normal subgroup of | #34181754, #34181757, #34194248, … |
| maximal quotient of | #34209384, #34209401, C4×#19098438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6994);