Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #450×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3323 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,f^c=fg770 conjugacy classes — view the full character table.
| maximal subgroup of | #3323×D79, C2×#23775620, #35165219, … |
| maximal normal subgroup of | #3323×D79, C2×#23775620, #35165219, … |
| maximal quotient of | #34303873, #34304680, #34305556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16730);