Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #442×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3318 |
462 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,f^c=fg,h^d=h^78887 conjugacy classes — view the full character table.
| maximal subgroup of | #3318×D79, C2×#23775546, #35165029, … |
| maximal normal subgroup of | #3318×D79, C2×#23775546, #35165029, … |
| maximal quotient of | #34303814, #34304592, #34305360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16656);