Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #452×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3011 |
700 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^c=h^78,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3011×D79, C2×#23772692, #35154732, … |
| maximal normal subgroup of | #3011×D79, C2×#23772692, #35154732, … |
| maximal quotient of | #34261459, #34261461, #34261547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13802);