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 ⋊ #3509 |
992 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180227, #34180231, #34180513, … |
| maximal normal subgroup of | #34180227, #34180231, #34180513, … |
| maximal quotient of | #34448413, #34448666, #34448718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18394);