Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #417×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3141 |
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,d^c=dg,h^c=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #34338641, #34338643, #34338645, … |
| maximal normal subgroup of | #34338641, #34338643, #34338645, … |
| maximal quotient of | #34288481, #34290971, #34290973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14901);