Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #441×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2947 |
470 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^78,d^c=dg,h^c=h^78,h^d=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #2947×D79, C2×#23772242, #35152385, … |
| maximal normal subgroup of | #2947×D79, C2×#23772242, #35152385, … |
| maximal quotient of | #34257717, #34257908, #34257927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13352);