Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×C79⋊C8 |
| Sylow | C79 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 296 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.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179032, #102×C79⋊C8, #34179039, … |
| maximal normal subgroup of | #34179032, #102×C79⋊C8, #34179039, … |
| maximal quotient of | C4⋊C8×C79⋊C8, #34179400, #34179416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4374);