Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^c=h^781640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C4⋊C4×D79, C2×#23763261, #34286216, … |
| maximal normal subgroup of | C8×C4⋊C4×D79, C2×#23763261, #34286216, … |
| maximal quotient of | #34179389, #34179397, #34179412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4371);