Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #504×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3416 |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^78,e^b=ef,f^b=fg,h^b=h^78,d^c=dg1592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34445020, #34445022, #34445027, … |
| maximal normal subgroup of | #34445020, #34445022, #34445027, … |
| maximal quotient of | #34441182, #34441189, #34441318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17658);