Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3461 |
1012 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,h^a=h^78,c^b=cf1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179682, #34179685, #34180065, … |
| maximal normal subgroup of | #34179682, #34179685, #34180065, … |
| maximal quotient of | #34446964, #34446977, #34447233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17943);