Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #330×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1532 |
218 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 59 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=fg,d^2=g,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^78,h^c=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #1532×D79, C2×#23762019, #34256208, … |
| maximal normal subgroup of | #1532×D79, C2×#23762019, #34256208, … |
| maximal quotient of | #34176290, #34176293, #34176320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3129);