Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #349×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1320 |
128 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=d,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=de,h^b=h^78,d^c=dg884 conjugacy classes — view the full character table.
| maximal subgroup of | #1320×D79, C2×#23761335, #34197389, … |
| maximal normal subgroup of | #1320×D79, C2×#23761335, #34197389, … |
| maximal quotient of | #34174887, #34174889, #34174899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2445);