Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19098967 |
| Sylow | C79 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #34206839, #34206843, #34206856, … |
| maximal normal subgroup of | #34206839, #34206843, #34206856, … |
| maximal quotient of | C2×#23763558, C2×#23764131, C2×#23764132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15017);