Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19098664 |
| Sylow | C79 ⋊ C2×#440 |
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19098664, #440×Dic79, #34286788, … |
| maximal normal subgroup of | C4×#19098664, #440×Dic79, #34286788, … |
| maximal quotient of | C2×SD16⋊(C79⋊C8), C2×#23762258, C2×#23762279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13290);