Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #1593 |
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,c^b=cg,d^b=df,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1593×D79, C2×#23762306, #34258041, … |
| maximal normal subgroup of | #1593×D79, C2×#23762306, #34258041, … |
| maximal quotient of | #34179109, #34179113, #34179527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3416);