Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#19098464 |
| Fitting | C22×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#390 |
1360 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34193630, #34194530, #34194540, … |
| maximal normal subgroup of | #34193630, #34194530, #34194540, … |
| maximal quotient of | C2×#23761629, C2×#23761636, C4×#19098464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6965);