Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #568×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3069 |
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^78,d^b=dg,f^c=fg1355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34325791, #34325796, #34325813, … |
| maximal normal subgroup of | #34325791, #34325796, #34325813, … |
| maximal quotient of | #34271048, #34271059, #34271092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14247);