Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #352×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2121 |
280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^b=h^78,h^c=h^78,e^d=eg530 conjugacy classes — view the full character table.
| maximal subgroup of | #2121×D79, C2×#23765045, #34441009, … |
| maximal normal subgroup of | #2121×D79, C2×#23765045, #34441009, … |
| maximal quotient of | #34197358, #34197445, #34197528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6155);