Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×Dic79 |
| Sylow | C79 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 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 | #329×Dic79, #34179193, #34179201, … |
| maximal normal subgroup of | #329×Dic79, #34179193, #34179201, … |
| maximal quotient of | #388×Dic79, #390×Dic79, #391×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7055);