Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19098966 |
| Sylow | C79 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #34183522, #34183523, #34183525, … |
| maximal normal subgroup of | #34183522, #34183523, #34183525, … |
| maximal quotient of | C2×#23763559, C2×#23764130, C2×#23764360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15016);