Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #341×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2080 |
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 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,c^2=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^78,c^b=cf,d^b=dg,e^b=eg,h^b=h^78,f^c=fg,h^c=h^781118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2080×D79, C2×#23764856, #34317194, … |
| maximal normal subgroup of | #2080×D79, C2×#23764856, #34317194, … |
| maximal quotient of | #34193041, #34193046, #34193051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5966);