Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #380×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1799 |
380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=d,b^a=bd,c^a=ce,e^a=eg,f^c=fg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179798, #34179801, #34179803, … |
| maximal normal subgroup of | #34179798, #34179801, #34179803, … |
| maximal quotient of | #34180923, #34180927, #34180931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4495);