Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D4⋊C8×D79 |
| Fitting | D4⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C2×D4⋊C8×D79, #1476×D79, #1478×D79, … |
| maximal normal subgroup of | C2×D4⋊C8×D79, #1476×D79, #1478×D79, … |
| maximal quotient of | #1270×D79, #1271×D79, #34176205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2881);