Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2993 |
354 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,d^b=dg,h^b=h^78,h^c=h^78,h^d=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34258330, #34258334, #34258345, … |
| maximal normal subgroup of | #34258330, #34258334, #34258345, … |
| maximal quotient of | #34287090, #34287131, #34287225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13658);