Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#131×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3067 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^78,f^c=fg1592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34205225, #34205227, #34205281, … |
| maximal normal subgroup of | #34205225, #34205227, #34205281, … |
| maximal quotient of | #34270511, #34270539, #34270579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14230);