Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | #336×D79 |
| Fitting | #336×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#336 |
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1270×D79, #1271×D79, #1272×D79, … |
| maximal normal subgroup of | #1270×D79, #1271×D79, #1272×D79, … |
| maximal quotient of | #1273×D79, #34177649, #34177653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4199);