Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #462×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3212 |
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^78,c^b=ce,h^b=h^78,f^c=fg,h^c=h^78,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #34265776, #34265778, #34265804, … |
| maximal normal subgroup of | #34265776, #34265778, #34265804, … |
| maximal quotient of | #34297600, #34297969, #34298815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15491);