Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #449×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3006 |
806 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^78,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3006×D79, C2×#23772649, #35154657, … |
| maximal normal subgroup of | #3006×D79, C2×#23772649, #35154657, … |
| maximal quotient of | #34260661, #34260700, #34260739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13759);