Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #341×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1855 |
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^78,d^b=dg,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1855×D79, C2×#23763606, #34289055, … |
| maximal normal subgroup of | #1855×D79, C2×#23763606, #34289055, … |
| maximal quotient of | #34182098, #34182103, #34182109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4716);