Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #389×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2042 |
318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 318 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=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,e^b=eg,f^b=fg,h^b=h^78,e^c=eg,f^c=fg1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2042×D79, C2×#23764641, #34315956, … |
| maximal normal subgroup of | #2042×D79, C2×#23764641, #34315956, … |
| maximal quotient of | #34191605, #34191612, #34191643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5751);