Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19098842 |
| Fitting | C2×#107×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#474 |
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19098842, #34295830, #34295903, … |
| maximal normal subgroup of | C4×#19098842, #34295830, #34295903, … |
| maximal quotient of | C2×#23763399, C2×#23763644, C2×#23763648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14254);