Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #340×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2067 |
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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=de,b^2=dg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,h^b=h^78,d^c=dg,e^c=eg,f^c=fg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2067×D79, C2×#23764789, #34316881, … |
| maximal normal subgroup of | #2067×D79, C2×#23764789, #34316881, … |
| maximal quotient of | #34192787, #34192794, #34192815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5899);