Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14579185 |
| Fitting | C22×D8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34289627, #34289651, #34289663, … |
| maximal normal subgroup of | #34289627, #34289651, #34289663, … |
| maximal quotient of | C22×#19098566, C22×#19098561, C22×#19098604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19241);