Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1992 |
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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=def,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cg,h^b=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175659, #34180714, #34180716, … |
| maximal normal subgroup of | #34175659, #34180714, #34180716, … |
| maximal quotient of | #34188283, #34188299, #34188346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5478);