Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×D4⋊(C79⋊C8) |
| Sylow | C79 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C4×D4⋊(C79⋊C8), D4⋊C8×Dic79, #34178871, … |
| maximal normal subgroup of | C4×D4⋊(C79⋊C8), D4⋊C8×Dic79, #34178871, … |
| maximal quotient of | C2×#23761221, C2×#23761223, #34176208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2883);