Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×#14579158 |
| Fitting | C43×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34176243, #34176324, #34176326, … |
| maximal normal subgroup of | #34176243, #34176324, #34176326, … |
| maximal quotient of | C4×#19098465, C4×#19098433, C4×#19098473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7075);