Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #568×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1881 |
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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=df,d^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^78,d^b=dg,f^b=fg,e^c=eg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1881×D79, C2×#23763762, #34289747, … |
| maximal normal subgroup of | #1881×D79, C2×#23763762, #34289747, … |
| maximal quotient of | #34182886, #34182893, #34182900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4872);