Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #382×D79 |
| Fitting | #382×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#382 |
712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1286×D79, #34178059, #1295×D79, … |
| maximal normal subgroup of | #1286×D79, #34178059, #1295×D79, … |
| maximal quotient of | #1434×D79, C4⋊#95×D79, #34209496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6894);