Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^78,d^b=dg1598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180457, #34180458, #34180471, … |
| maximal normal subgroup of | #34180457, #34180458, #34180471, … |
| maximal quotient of | #34179645, #34179658, #34179719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4450);