Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #1374 |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175012, #34175013, #34175035, … |
| maximal normal subgroup of | #34175012, #34175013, #34175035, … |
| maximal quotient of | #34175097, #34175111, #34175118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2588);